A297434 Number of 4 X n 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2 neighboring 1s.

1, 4, 22, 42, 105, 349, 1057, 2834, 8216, 24556, 71651, 207409, 608985, 1791636, 5251548, 15401954, 45271039, 133066199, 390990659, 1149260888, 3379206474, 9935995300, 29215600841, 85913309363, 252656693545, 743030170284

Offset

1,2

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) + a(n-4) - 33*a(n-5) - 7*a(n-6) + 21*a(n-7) + 3*a(n-8) + 2*a(n-9) + 3*a(n-10) + 5*a(n-11) - 2*a(n-12).

Empirical g.f.: x*(1 + x + 9*x^2 - 28*x^3 - 44*x^4 + 21*x^5 + 22*x^6 + 5*x^7 + 5*x^8 + 8*x^9 + 3*x^10 - 2*x^11) / ((1 + x)*(1 - 4*x + 3*x^2 - 3*x^3 + 2*x^4 + 31*x^5 - 24*x^6 + 3*x^7 - 6*x^8 + 4*x^9 - 7*x^10 + 2*x^11)). - Colin Barker, Feb 28 2019

Example

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

Crossrefs

Row 4 of A297431.

Sequence in context: A350521 A163484 A326737 * A020173 A290709 A163433

Adjacent sequences: A297431 A297432 A297433 * A297435 A297436 A297437

Keyword

nonn

Author

R. H. Hardin, Dec 30 2017

Status

approved