A296645 - OEIS

A296645

Number of n X 2 0..1 arrays with each 1 adjacent to 0, 1 or 3 king-move neighboring 1s.

4, 12, 29, 85, 248, 664, 1897, 5385, 14924, 42180, 118869, 332765, 937088, 2635856, 7400673, 20815825, 58523540, 164457532, 462389261, 1299858917, 3653657736, 10271361928, 28873923801, 81164992281, 228166526044, 641398040884

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OFFSET

1,1

LINKS

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

FORMULA

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

Empirical g.f.: x*(4 + 8*x + 5*x^2 - 16*x^3 - 16*x^4 - 4*x^5) / (1 - x - 3*x^2 - 9*x^3 + 4*x^4 + 12*x^5 + 4*x^6). - Colin Barker, Feb 23 2019

EXAMPLE

Some solutions for n=7:

..0..0. .0..1. .0..0. .0..0. .0..0. .0..0. .1..0. .1..0. .0..0. .1..0

..1..0. .0..0. .0..1. .1..0. .0..0. .0..0. .0..1. .0..0. .0..1. .1..0

..0..0. .1..0. .0..1. .0..0. .1..1. .0..1. .0..0. .0..1. .0..1. .0..0

..1..1. .1..0. .1..1. .0..0. .1..1. .0..0. .0..0. .0..0. .1..1. .0..0

..0..0. .0..0. .1..0. .0..0. .0..0. .0..1. .1..0. .0..0. .0..1. .0..0

..1..1. .1..1. .0..1. .1..1. .0..0. .0..0. .0..0. .0..0. .0..1. .0..1

..1..1. .1..1. .0..0. .0..0. .0..1. .1..0. .1..1. .1..1. .0..0. .0..1

CROSSREFS

Column 2 of A296651.

Sequence in context: A036889 A036895 A309297 * A280007 A061726 A067706

Adjacent sequences: A296642 A296643 A296644 * A296646 A296647 A296648

KEYWORD

nonn

AUTHOR

R. H. Hardin, Dec 17 2017

STATUS

approved