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Search: a096252 -id:a096252
Displaying 1-4 of 4 results found.
page 1
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A298924
T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero.
+10
7
0, 1, 1, 0, 4, 0, 1, 4, 4, 1, 0, 8, 1, 8, 0, 1, 32, 2, 2, 32, 1, 0, 32, 3, 3, 3, 32, 0, 1, 64, 5, 7, 7, 5, 64, 1, 0, 256, 8, 6, 9, 6, 8, 256, 0, 1, 256, 16, 9, 12, 12, 9, 16, 256, 1, 0, 512, 21, 20, 17, 19, 17, 20, 21, 512, 0, 1, 2048, 34, 22, 41, 22, 22, 41, 22, 34, 2048, 1, 0, 2048, 55, 35, 42
(list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,5
COMMENTS
Table starts
.0...1..0..1..0..1..0...1...0...1....0....1....0.....1.....0.....1......0
.1...4..4..8.32.32.64.256.256.512.2048.2048.4096.16384.16384.32768.131072
.0...4..1..2..3..5..8..16..21..34...55...89..144...236...377...610....987
.1...8..2..3..7..6..9..20..22..35...59...90..145...240...378...611....991
.0..32..3..7..9.12.17..41..42..67..109..172..277...461...722..1167...1889
.1..32..5..6.12.19.22..48..53.103..169..272..446...863..1346..2395...4154
.0..64..8..9.17.22.31..83..92.172..309..549..923..1830..3021..5580..10091
.1.256.16.20.41.48.83.199.225.460..943.1570.2795..5933.10113.19462..37621
.0.256.21.22.42.53.92.225.330.644.1348.2306.4339..9315.17574.35170..70446
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..543
FORMULA
Empirical for column k:
k=1: a(n) = a(n-2)
k=2: a(n) = 8*a(n-3)
k=3: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8)
k=4: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8)
k=5: a(n) = a(n-1) +a(n-2) +a(n-6) -a(n-7) -a(n-8) for n>11
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..0..0..0..0. .0..0..1..1. .1..1..0..0. .0..0..0..0. .0..0..1..1
..1..1..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
..1..1..1..1. .0..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..1..0
CROSSREFS
Column 2 is A096252(n-1).
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 29 2018
STATUS
approved
A299451
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6 or 8 king-move adjacent elements, with upper left element zero.
+10
7
1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 8, 1, 8, 8, 13, 32, 4, 4, 32, 13, 21, 32, 10, 21, 10, 32, 21, 34, 64, 6, 32, 32, 6, 64, 34, 55, 256, 11, 36, 231, 36, 11, 256, 55, 89, 256, 41, 161, 163, 163, 161, 41, 256, 89, 144, 512, 24, 264, 546, 211, 546, 264, 24, 512, 144, 233, 2048, 42, 430
(list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1...2..3...5....8...13....21.....34.....55......89......144.......233
..2...4..4...8...32...32....64....256....256.....512.....2048......2048
..3...4..1...4...10....6....11.....41.....24......42......169.......100
..5...8..4..21...32...36...161....264....430....1475.....2598......4872
..8..32.10..32..231..163...546...2904...2321....8729....37095.....34873
.13..32..6..36..163..211...804...3138...4869...21921....69029....124071
.21..64.11.161..546..804..6326..19745..39495..290364...855008...2191987
.34.256.41.264.2904.3138.19745.174794.205522.1778833.11489465..16992517
.55.256.24.430.2321.4869.39495.205522.665961.5936888.26103440.114805573
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..241
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 8*a(n-3) for n>4
k=3: [order 18] for n>19
k=4: [order 62] for n>63
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..0..1..1. .0..1..1..0. .0..0..0..1. .0..1..1..0
..1..1..1..1. .0..0..1..1. .1..0..1..1. .0..0..0..1. .0..1..1..0
..0..1..1..1. .0..0..0..0. .1..1..1..0. .1..1..0..0. .1..1..1..1
..1..1..0..0. .1..1..0..0. .0..1..1..1. .0..0..0..1. .1..0..0..1
..0..1..1..1. .1..1..0..0. .1..0..1..0. .0..0..0..1. .1..0..0..1
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A096252(n-1).
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 10 2018
STATUS
approved
A300089
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.
+10
7
1, 2, 2, 3, 4, 3, 5, 4, 4, 5, 8, 8, 1, 8, 8, 13, 32, 4, 4, 32, 13, 21, 32, 10, 25, 10, 32, 21, 34, 64, 6, 50, 50, 6, 64, 34, 55, 256, 19, 98, 415, 98, 19, 256, 55, 89, 256, 41, 359, 533, 533, 359, 41, 256, 89, 144, 512, 32, 766, 3089, 1822, 3089, 766, 32, 512, 144, 233, 2048, 106
(list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
..1...2..3....5.....8.....13......21........34.........55..........89
..2...4..4....8....32.....32......64.......256........256.........512
..3...4..1....4....10......6......19........41.........32.........106
..5...8..4...25....50.....98.....359.......766.......1932........5677
..8..32.10...50...415....533....3089.....13808......27523......150838
.13..32..6...98...533...1822...13646.....64560.....292356.....1935206
.21..64.19..359..3089..13646..167131...1179926....7203918....75245386
.34.256.41..766.13808..64560.1179926..14634300..102798960..1708342471
.55.256.32.1932.27523.292356.7203918.102798960.1518807971.32115302281
LINKS
R. H. Hardin, Table of n, a(n) for n = 1..220
FORMULA
Empirical for column k:
k=1: a(n) = a(n-1) +a(n-2)
k=2: a(n) = 8*a(n-3) for n>4
k=3: [order 20] for n>21
k=4: [order 59] for n>61
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..0..0..1..1. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .1..1..1..1
..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..1. .1..1..1..1
..0..0..0..0. .1..1..0..0. .1..1..0..0. .0..0..0..1. .1..1..1..1
CROSSREFS
Column 1 is A000045(n+1).
Column 2 is A096252(n-1).
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Feb 24 2018
STATUS
approved
A137717
Hankel transform of A106191.
+10
3
1, -4, 4, 8, -32, 32, 64, -256, 256, 512, -2048, 2048, 4096, -16384, 16384, 32768, -131072, 131072, 262144, -1048576, 1048576, 2097152, -8388608, 8388608, 16777216, -67108864, 67108864, 134217728, -536870912, 536870912
(list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Hankel transform of A132310. [From Paul Barry, Apr 26 2009]
LINKS
Table of n, a(n) for n=0..29.
Index entries for linear recurrences with constant coefficients, signature (-2,-4).
FORMULA
G.f.: (1-2x)/(1+2x+4x^2).
a(n)=Product{k=0..n, (3*cos(2*pi*(k-1)/3)/2-5/4-2*0^k)^(n-k)};
a(n) = 2^n*A061347(n+2) = -2a(n-1)-4a(n-2). - R. J. Mathar, Feb 21 2008
MATHEMATICA
LinearRecurrence[{-2, -4}, {1, -4}, 30] (* Harvey P. Dale, Oct 05 2017 *)
CROSSREFS
Apart from signs, essentially the same as A096252.
KEYWORD
sign
AUTHOR
Paul Barry, Feb 08 2008
STATUS
approved
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