A298924 - OEIS

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.

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

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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. .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

CROSSREFS

Column 2 is A096252(n-1).

Sequence in context: A124321 A232195 A309333 * A217476 A298622 A298454

Adjacent sequences: A298921 A298922 A298923 * A298925 A298926 A298927

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 29 2018

STATUS

approved