A298141 Number of n X 3 0..1 arrays with every element equal to 2, 3, 6 or 7 king-move adjacent elements, with upper left element zero.

0, 2, 0, 2, 1, 6, 8, 15, 22, 44, 82, 152, 267, 486, 898, 1675, 3088, 5686, 10512, 19530, 36309, 67442, 125268, 232951, 433598, 807304, 1503082, 2798968, 5213647, 9713698, 18099774, 33727651, 62853728, 117142090, 218334832, 406958706, 758560313

Offset

1,2

Comments

Column 3 of A298146.

Links

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

Formula

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

Empirical g.f.: x^2*(1 - x)*(2 - 2*x^2 - 3*x^3 - 2*x^4 - 6*x^5 - 3*x^6) / ((1 + x)*(1 - 2*x - 2*x^5 + 6*x^6 + 2*x^7 - x^8)). - Colin Barker, Mar 22 2018

Example

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

Crossrefs

Cf. A298146.

Sequence in context: A354158 A363580 A196517 * A160210 A174610 A375108

Adjacent sequences: A298138 A298139 A298140 * A298142 A298143 A298144

Keyword

nonn

Author

R. H. Hardin, Jan 13 2018

Status

approved