A299942 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 25, 25, 8, 16, 85, 70, 85, 16, 32, 286, 205, 205, 286, 32, 64, 969, 614, 649, 614, 969, 64, 128, 3281, 1860, 2153, 2153, 1860, 3281, 128, 256, 11114, 5631, 7016, 8379, 7016, 5631, 11114, 256, 512, 37649, 17034, 22819, 30204, 30204, 22819

Offset

1,2

Comments

Table starts

...1.....2.....4......8......16......32.......64.......128........256

...2.....8....25.....85.....286.....969.....3281.....11114......37649

...4....25....70....205.....614....1860.....5631.....17034......51507

...8....85...205....649....2153....7016....22819.....73931.....239461

..16...286...614...2153....8379...30204...106323....379361....1353507

..32...969..1860...7016...30204..124748...495413...2007099....8185319

..64..3281..5631..22819..106323..495413..2237911..10459697...49578223

.128.11114.17034..73931..379361.2007099.10459697..57942564..326734318

.256.37649.51507.239461.1353507.8185319.49578223.326734318.2226744922

Links

R. H. Hardin, Table of n, a(n) for n = 1..263

Formula

Empirical for column k:

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

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

k=3: [order 11] for n>12

k=4: [order 22] for n>28

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281338.

Column 3 is A298282.

Column 4 is A299176.

Sequence in context: A298287 A299359 A299180 * A301841 A302069 A298195

Adjacent sequences: A299939 A299940 A299941 * A299943 A299944 A299945

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 22 2018

Status

approved