A299142 T(n,k) = Number of n X k 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

0, 1, 1, 1, 4, 1, 2, 18, 18, 2, 3, 64, 129, 64, 3, 5, 236, 899, 899, 236, 5, 8, 888, 6205, 11179, 6205, 888, 8, 13, 3336, 43066, 143548, 143548, 43066, 3336, 13, 21, 12512, 298361, 1850266, 3426869, 1850266, 298361, 12512, 21, 34, 46928, 2068149

Offset

1,5

Comments

Table starts

..0.....1........1..........2.............3...............5.................8

..1.....4.......18.........64...........236.............888..............3336

..1....18......129........899..........6205...........43066............298361

..2....64......899......11179........143548.........1850266..........23808476

..3...236.....6205.....143548.......3426869........81988764........1958821107

..5...888....43066....1850266......81988764......3643124959......161617794805

..8..3336...298361...23808476....1958821107....161617794805....13311860331263

.13.12512..2068149..306389599...46801360032...7170422794173..1096571119921011

.21.46928.14334327.3942948157.1118229413140.318133492126048.90332592148780928

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 10] for n>11.

k=4: [order 33] for n>34.

Example

Some solutions for n=5, k=4
..0..0..1..0. .0..0..0..0. .0..0..1..1. .0..0..0..0. .0..0..0..0
..1..0..0..1. .0..1..0..0. .1..1..1..0. .0..0..1..0. .0..1..0..1
..0..1..0..1. .0..1..1..0. .0..0..0..1. .0..0..0..1. .1..0..1..0
..0..1..0..0. .0..0..1..1. .0..0..1..0. .1..1..0..1. .0..1..0..1
..0..1..1..1. .0..0..0..1. .1..1..0..0. .1..0..0..1. .1..0..0..0

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A231950(n-1).

Sequence in context: A299465 A300108 A298280 * A299373 A299937 A299067

Adjacent sequences: A299139 A299140 A299141 * A299143 A299144 A299145

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 03 2018

Status

approved