A296536 Number of n X 3 0..1 arrays with each 1 horizontally, vertically or antidiagonally adjacent to 2 or 4 neighboring 1s.

1, 5, 16, 37, 96, 254, 654, 1709, 4472, 11621, 30257, 78899, 205534, 535394, 1395017, 3634476, 9468722, 24669483, 64272370, 167449745, 436262198, 1136608103, 2961236309, 7714995835, 20100110050, 52367403411, 136434332477, 355456392933

Offset

1,2

Links

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

Formula

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

Empirical g.f.: x*(1 + 3*x + 7*x^2 + 5*x^3 + 12*x^4 + 8*x^5 + 4*x^6 + 6*x^7 - 7*x^9 - 5*x^10 - x^11) / ((1 + x^2 + x^3)*(1 - 2*x - 4*x^3 + x^4 - 2*x^5 - 4*x^6 + 3*x^8 + x^9)). - Colin Barker, Feb 23 2019

Example

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

Crossrefs

Column 3 of A296541.

Sequence in context: A274248 A188427 A022496 * A041044 A042645 A218259

Adjacent sequences: A296533 A296534 A296535 * A296537 A296538 A296539

Keyword

nonn

Author

R. H. Hardin, Dec 15 2017

Status

approved