A299180 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 6 or 7 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, 8368, 7016, 5631, 11114, 256, 512, 37649, 17034, 22819, 30089, 30089, 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....8368...30089...105709....376826....1341575

..32...969..1860...7016...30089..123258...488812...1973932....7998917

..64..3281..5631..22819..105709..488812..2207509..10286880...48492179

.128.11114.17034..73931..376826.1973932.10286880..56481101..314537796

.256.37649.51507.239461.1341575.7998917.48492179.314537796.2090883077

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

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=5
..0..0..1..0..1. .0..1..1..0..1. .0..0..1..0..1. .0..1..1..0..0
..1..0..0..1..0. .0..1..1..0..1. .1..1..1..1..0. .0..1..1..0..1
..0..0..0..0..1. .1..1..1..1..1. .1..1..1..1..1. .1..1..1..1..1
..1..0..0..0..0. .0..1..1..1..0. .0..0..1..1..0. .0..1..1..1..0
..0..1..0..1..0. .1..1..0..1..1. .0..1..0..1..1. .1..1..0..1..1

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A281338.

Column 3 is A298282.

Sequence in context: A281344 A298287 A299359 * A299942 A301841 A302069

Adjacent sequences: A299177 A299178 A299179 * A299181 A299182 A299183

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 04 2018

Status

approved