A295980 Number of n X 3 0..1 arrays with each 1 adjacent to 2 or 3 king-move neighboring 1s.

1, 15, 44, 110, 581, 2354, 8452, 35474, 146560, 580023, 2356053, 9619854, 38867687, 157518881, 639985423, 2594957421, 10522265148, 42696678744, 173200350255, 702516695938, 2849908304750, 11560960945608, 46896382885056

Offset

1,2

Links

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

Formula

Empirical: a(n) = 4*a(n-1) - 2*a(n-2) + 21*a(n-3) - 44*a(n-4) - 12*a(n-5) - 34*a(n-6) + 33*a(n-7) + 4*a(n-8) + 14*a(n-9) + a(n-10).

Empirical g.f.: x*(1 + 11*x - 14*x^2 - 57*x^3 - 42*x^4 - 2*x^5 + 38*x^6 + 18*x^7 + 15*x^8 + x^9) / (1 - 4*x + 2*x^2 - 21*x^3 + 44*x^4 + 12*x^5 + 34*x^6 - 33*x^7 - 4*x^8 - 14*x^9 - x^10). - Colin Barker, Feb 22 2019

Example

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

Crossrefs

Column 3 of A295985.

Sequence in context: A364081 A292018 A289669 * A029827 A357706 A119123

Adjacent sequences: A295977 A295978 A295979 * A295981 A295982 A295983

Keyword

nonn

Author

R. H. Hardin, Dec 01 2017

Status

approved