A298177 - OEIS

A298177

T(n,k)=Number of nXk 0..1 arrays with every element equal to 2, 3, 6 or 8 king-move adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 1, 0, 0, 8, 2, 2, 8, 0, 0, 5, 1, 8, 1, 5, 0, 0, 22, 6, 13, 13, 6, 22, 0, 0, 29, 8, 27, 34, 27, 8, 29, 0, 0, 60, 15, 43, 57, 57, 43, 15, 60, 0, 0, 121, 22, 104, 73, 87, 73, 104, 22, 121, 0, 0, 194, 44, 220, 174, 161, 161, 174, 220, 44, 194, 0, 0, 425, 82

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,8

COMMENTS

Table starts

.0..0..0...0...0...0....0....0....0.....0.....0.....0......0......0......0

.0..1..2...1...8...5...22...29...60...121...194...425....704...1421...2574

.0..2..0...2...1...6....8...15...22....44....82...152....267....486....898

.0..1..2...8..13..27...43..104..220...478...988..2085...4451...9505..20311

.0..8..1..13..34..57...73..174..350...800..1605..3376...7079..15234..32785

.0..5..6..27..57..87..161..361..898..1984..4089..8938..20136..45253.100907

.0.22..8..43..73.161..181..540.1076..2572..5179.11814..27638..63592.145715

.0.29.15.104.174.361..540.1380.2682..6043.12820.28413..61050.133945.294724

.0.60.22.220.350.898.1076.2682.4176.11358.21477.51492.105048.245900.540109

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..511

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 3*a(n-2) +2*a(n-3) -2*a(n-4)

k=3: a(n) = a(n-1) +2*a(n-2) +2*a(n-5) -4*a(n-6) -8*a(n-7) -a(n-8) +a(n-9)

k=4: [order 21] for n>27

k=5: [order 34] for n>40

k=6: [order 67] for n>74

EXAMPLE

Some solutions for n=7 k=4

..0..0..1..1. .0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..1..1

..0..1..0..1. .1..0..0..1. .0..1..1..0. .0..1..1..0. .0..1..0..1

..0..1..0..1. .1..1..1..0. .0..1..0..1. .0..1..0..1. .0..1..0..1

..0..1..0..1. .0..0..0..1. .0..1..0..1. .0..1..0..1. .1..0..1..0

..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..1..0..1. .1..0..1..0

..0..1..0..1. .1..0..0..1. .1..0..1..0. .0..1..1..0. .0..1..1..0

..0..0..1..1. .1..1..1..1. .1..1..0..0. .0..0..0..0. .0..0..0..0

CROSSREFS

Column 2 is A297809.

Column 3 is A298141.

Column 4 is A298142.

Column 5 is A298143.

Sequence in context: A141612 A316342 A297814 * A298146 A295520 A295335

Adjacent sequences: A298174 A298175 A298176 * A298178 A298179 A298180

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 14 2018

STATUS

approved