A299593 Number of n X 6 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

13, 15, 35, 121, 256, 576, 1225, 2601, 5625, 12100, 25921, 55696, 119716, 257049, 552049, 1185921, 2547216, 5470921, 11751184, 25240576, 54213769, 116445681, 250114225, 537219684, 1153892961, 2478446656, 5323453444, 11434238761

Offset

1,1

Comments

Column 6 of A299595.

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>9.

Empirical g.f.: x*(13 + 2*x + 7*x^2 + 32*x^3 + 42*x^4 + 92*x^5 + 23*x^6 - 39*x^7 - 29*x^8) / ((1 + x^2 - x^3)*(1 - x - 2*x^2 - x^3)). - Colin Barker, Feb 15 2018

Example

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

Crossrefs

Cf. A299595.

Sequence in context: A113801 A108257 A217252 * A318543 A302001 A109018

Adjacent sequences: A299590 A299591 A299592 * A299594 A299595 A299596

Keyword

nonn

Author

R. H. Hardin, Feb 13 2018

Status

approved