A297954 Number of n X 3 0..1 arrays with every element equal to 1, 2, 4 or 5 king-move adjacent elements, with upper left element zero.

1, 7, 15, 25, 47, 109, 245, 545, 1253, 2859, 6557, 15131, 34879, 80643, 186663, 432253, 1002043, 2323805, 5391149, 12511905, 29043489, 67430735, 156577101, 363614071, 844480819, 1961394067, 4555748943, 10582066605, 24580613559, 57098398457

Offset

1,2

Comments

Column 3 of A297959.

Links

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

Formula

Empirical: a(n) = 2*a(n-1) + 2*a(n-2) + a(n-3) - 8*a(n-4) - 2*a(n-5) - 2*a(n-6) + 2*a(n-7) - a(n-8) + 2*a(n-9) + 3*a(n-11) + 2*a(n-12) for n>13.

Empirical g.f.: x*(1 - 2*x)*(1 + 7*x + 13*x^2 + 6*x^3 - 20*x^4 - 32*x^5 - 20*x^6 - 8*x^7 - 9*x^8 - 9*x^9 - 7*x^10 - 2*x^11) / ((1 - x)*(1 - x - 3*x^2 - 4*x^3 + 4*x^4 + 6*x^5 + 8*x^6 + 6*x^7 + 7*x^8 + 5*x^9 + 5*x^10+ 2*x^11)). - Colin Barker, Mar 22 2018

Example

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

Crossrefs

Cf. A297959.

Sequence in context: A323483 A236582 A268662 * A298577 A299569 A260558

Adjacent sequences: A297951 A297952 A297953 * A297955 A297956 A297957

Keyword

nonn

Author

R. H. Hardin, Jan 09 2018

Status

approved