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A299574 T(n,k)=Number of nXk 0..1 arrays with every element equal to 1, 2, 4, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 3, 1, 2, 7, 7, 2, 3, 13, 15, 13, 3, 5, 23, 25, 25, 23, 5, 8, 49, 47, 78, 47, 49, 8, 13, 99, 113, 237, 237, 113, 99, 13, 21, 189, 265, 844, 766, 844, 265, 189, 21, 34, 383, 621, 2604, 3324, 3324, 2604, 621, 383, 34, 55, 777, 1473, 8136, 15186, 17389, 15186, 8136 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0...1....1.....2......3.......5........8........13.........21..........34

..1...3....7....13.....23......49.......99.......189........383.........777

..1...7...15....25.....47.....113......265.......621.......1473........3443

..2..13...25....78....237.....844.....2604......8136......26760.......86924

..3..23...47...237....766....3324....15186.....56870.....234074.....1011095

..5..49..113...844...3324...17389....98466....505680....2704280....14896422

..8..99..265..2604..15186...98466...784334...5286269...38000347...284230090

.13.189..621..8136..56870..505680..5286269..46965400..449355259..4443621368

.21.383.1473.26760.234074.2704280.38000347.449355259.5736969146.75908899351

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2)

k=2: a(n) = 2*a(n-1) -a(n-2) +4*a(n-3) -4*a(n-4) for n>5

k=3: [order 14] for n>15

k=4: [order 67] for n>68

EXAMPLE

Some solutions for n=6 k=7

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

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A297953.

Sequence in context: A297959 A298775 A298582 * A298396 A299514 A299314

Adjacent sequences:  A299571 A299572 A299573 * A299575 A299576 A299577

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Feb 13 2018

STATUS

approved

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Last modified August 16 05:42 EDT 2022. Contains 356161 sequences. (Running on oeis4.)