A299589 Number of n X n 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 5, 23, 113, 576, 2583, 11656, 54738, 252959, 1159927, 5359097, 24760544, 114126327, 526426848, 2429504050, 11207820807, 51702119063, 238537489057, 1100501704736, 5077031912807, 23422773519432, 108060889914594

Offset

1,3

Comments

Diagonal of A299595.

Links

R. H. Hardin, Table of n, a(n) for n = 1..70

Formula

Empirical: a(n) = 3*a(n-1) +2*a(n-2) +28*a(n-3) -2*a(n-4) -42*a(n-5) -56*a(n-6) +50*a(n-7) -44*a(n-8) +30*a(n-9) -44*a(n-10) +2*a(n-11) +2*a(n-12) -a(n-14) +a(n-15) for n>18.

Example

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

Crossrefs

Cf. A299595.

Sequence in context: A186652 A199312 A320326 * A113284 A104090 A355055

Adjacent sequences: A299586 A299587 A299588 * A299590 A299591 A299592

Keyword

nonn

Author

R. H. Hardin, Feb 13 2018

Status

approved