A299592 Number of n X 5 0..1 arrays with every element unequal to 0, 1 or 4 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

8, 8, 19, 53, 113, 256, 541, 1148, 2488, 5349, 11453, 24617, 52916, 113605, 243988, 524156, 1125805, 2417997, 5193737, 11155712, 23961101, 51466060, 110544232, 237437573, 509991637, 1095411153, 2352832580, 5053645925, 10854721796

Offset

1,1

Comments

Column 5 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*(8 + 3*x^2 + 2*x^3 + 9*x^4 + 33*x^5 + 10*x^6 - 14*x^7 - 10*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..1..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..0..0. .1..0..0..0..0. .0..0..0..0..1
..0..0..0..0..0. .1..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. .1..0..0..0..0
..0..0..1..0..0. .0..1..0..0..0. .0..1..0..0..0. .0..0..0..1..0

Crossrefs

Cf. A299595.

Sequence in context: A298166 A298956 A232652 * A339707 A061156 A359037

Adjacent sequences: A299589 A299590 A299591 * A299593 A299594 A299595

Keyword

nonn

Author

R. H. Hardin, Feb 13 2018

Status

approved