A297514 Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 3 neighboring 1s.

3, 17, 49, 177, 727, 2445, 8931, 33841, 120079, 438161, 1618767, 5849585, 21333063, 78146401, 284124279, 1036090465, 3784306647, 13787045553, 50277043559, 183451730433, 668806025271, 2438991559953, 8896352148007, 32440479868961

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + 30*a(n-3) + 6*a(n-5) - 124*a(n-6) - 8*a(n-8) + 64*a(n-9).

Empirical g.f.: x*(3 + 14*x + 26*x^2 + 4*x^3 - 58*x^4 - 124*x^5 - 8*x^6 + 24*x^7 + 64*x^8) / (1 - x - 2*x^2 - 30*x^3 - 6*x^5 + 124*x^6 + 8*x^8 - 64*x^9). - Colin Barker, Feb 28 2019

Example

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

Crossrefs

Column 3 of A297519.

Sequence in context: A154304 A144640 A084069 * A307862 A132124 A011917

Adjacent sequences: A297511 A297512 A297513 * A297515 A297516 A297517

Keyword

nonn

Author

R. H. Hardin, Dec 31 2017

Status

approved