A278275 Number of n X 3 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) or (1,0), with upper left element zero.

0, 4, 25, 136, 839, 5013, 30370, 183403, 1108525, 6699034, 40484839, 244664745, 1478598250, 8935711959, 54001778309, 326352531078, 1972267883095, 11919137270093, 72031712514698, 435314024068379, 2630762103695997

Offset

1,2

Links

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

Formula

Empirical: a(n) = 6*a(n-1) + 3*a(n-2) - 17*a(n-3) + 19*a(n-5) - 16*a(n-6) + 8*a(n-7) for n>9.

Empirical g.f.: x^2*(1 - x)*(4 + 5*x - 21*x^2 - 5*x^3 - 9*x^4 + 2*x^5 - 2*x^6) / (1 - 6*x - 3*x^2 + 17*x^3 - 19*x^5 + 16*x^6 - 8*x^7). - Colin Barker, Feb 09 2019

Example

Some solutions for n=4:
..0..0..1. .0..1..1. .0..1..1. .0..1..1. .0..1..0. .0..0..1. .0..0..0
..1..1..1. .0..0..0. .0..0..0. .0..0..0. .0..1..0. .1..1..1. .1..1..1
..1..1..1. .1..0..1. .0..1..1. .1..1..1. .1..0..1. .1..1..0. .0..0..0
..0..0..0. .1..0..1. .0..0..1. .0..0..0. .0..0..0. .0..0..0. .0..1..1

Crossrefs

Column 3 of A278280.

Sequence in context: A220381 A015533 A207410 * A301836 A275177 A079291

Adjacent sequences: A278272 A278273 A278274 * A278276 A278277 A278278

Keyword

nonn

Author

R. H. Hardin, Nov 16 2016

Status

approved