A297310 Number of n X 4 0..1 arrays with every 1 horizontally or antidiagonally adjacent to 1 or 2 neighboring 1s.

7, 66, 497, 3808, 29212, 223995, 1717882, 13174266, 101033369, 774822892, 5942100272, 45569854023, 349474289622, 2680111429330, 20553721242845, 157626080234992, 1208831279237072, 9270503076704855, 71095304015354510

Offset

1,1

Links

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

Formula

Empirical: a(n) = 4*a(n-1) + 26*a(n-2) + 22*a(n-3) - 43*a(n-4) - a(n-5) + 7*a(n-6) - a(n-7) - a(n-8) for n>9.

Empirical g.f.: x*(7 + 38*x + 51*x^2 - 50*x^3 - 93*x^4 + 50*x^5 + 2*x^6 - 10*x^7 + x^8) / ((1 - 7*x - 5*x^2 - x^3)*(1 + 3*x - 6*x^3 + 4*x^4 - x^5)). - Colin Barker, Feb 26 2019

Example

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

Crossrefs

Column 4 of A297314.

Sequence in context: A239984 A274822 A179880 * A371780 A065097 A300991

Adjacent sequences: A297307 A297308 A297309 * A297311 A297312 A297313

Keyword

nonn

Author

R. H. Hardin, Dec 28 2017

Status

approved