A297596 Number of 3 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.

1, 9, 25, 49, 145, 443, 1141, 3009, 8455, 23151, 62211, 169651, 464469, 1262947, 3434407, 9364725, 25517397, 69467533, 189209921, 515479315, 1403998341, 3823905513, 10415880295, 28371283095, 77275911315, 210482481315

Offset

1,2

Links

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

Formula

Empirical: a(n) = a(n-1) + a(n-2) + 8*a(n-3) + 7*a(n-4) - 8*a(n-6) - 6*a(n-7).

Empirical g.f.: x*(1 + 8*x + 15*x^2 + 7*x^3 - 8*x^4 - 14*x^5 - 6*x^6) / (1 - x - x^2 - 8*x^3 - 7*x^4 + 8*x^6 + 6*x^7). - Colin Barker, Mar 01 2019

Example

Some solutions for n=7:
..1..0..0..1..1..0..0. .0..0..0..1..1..0..0. .1..0..1..0..0..0..0
..0..1..0..0..0..0..0. .0..1..0..0..0..0..0. .1..1..1..0..0..1..0
..0..0..0..0..0..0..0. .1..0..0..0..0..1..1. .1..0..0..0..0..0..1

Crossrefs

Row 3 of A297595.

Sequence in context: A282631 A245694 A045972 * A266132 A112629 A225322

Adjacent sequences: A297593 A297594 A297595 * A297597 A297598 A297599

Keyword

nonn

Author

R. H. Hardin, Jan 01 2018

Status

approved