A298282 Number of n X 3 0..1 arrays with every element equal to 0, 1, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

4, 25, 70, 205, 614, 1860, 5631, 17034, 51507, 155755, 471038, 1424553, 4308225, 13029159, 39403450, 119165999, 360388207, 1089905354, 3296150132, 9968393611, 30146949453, 91172018210, 275727297765, 833869252932, 2521832029371

Offset

1,1

Comments

Column 3 of A298287.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) - a(n-2) + 2*a(n-3) + 4*a(n-4) - a(n-5) + 2*a(n-6) - 2*a(n-7) - 3*a(n-8) - 2*a(n-9) - 2*a(n-10) - 2*a(n-11) for n>12.

Empirical g.f.: x*(4 + 13*x - x^2 + 12*x^3 + 3*x^4 - 13*x^5 - 8*x^6 - 19*x^7 - 13*x^8 - 7*x^9 - 2*x^10 - 4*x^11) / (1 - 3*x + x^2 - 2*x^3 - 4*x^4 + x^5 - 2*x^6 + 2*x^7 + 3*x^8 + 2*x^9 + 2*x^10 + 2*x^11). - Colin Barker, Feb 26 2018

Example

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

Crossrefs

Cf. A298287.

Sequence in context: A302324 A303017 A281339 * A077205 A180569 A302821

Adjacent sequences: A298279 A298280 A298281 * A298283 A298284 A298285

Keyword

nonn

Author

R. H. Hardin, Jan 16 2018

Status

approved