A297981 Number of n X 3 0..1 arrays with every element equal to 0, 2, 3 or 6 king-move adjacent elements, with upper left element zero.

1, 6, 2, 5, 7, 14, 21, 41, 70, 129, 233, 428, 783, 1445, 2664, 4933, 9137, 16956, 31495, 58557, 108952, 202837, 377797, 703972, 1312155, 2446433, 4562176, 8509137, 15873089, 29613308, 55252631, 103098397, 192387744, 359025085, 670023141

Offset

1,2

Comments

Column 3 of A297986.

Links

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

Formula

Empirical: a(n) = a(n-1) + 2*a(n-2) + a(n-3) - a(n-4) - 4*a(n-6) - 8*a(n-7) - 2*a(n-8) + 4*a(n-9) + 6*a(n-10) + 2*a(n-11) for n>13.

Empirical g.f.: x*(1 + 5*x - 6*x^2 - 10*x^3 - 7*x^4 + x^5 - 6*x^6 + 22*x^7 + 38*x^8 + 14*x^9 - 14*x^10 - 16*x^11 - 4*x^12) / ((1 - x)*(1 + x)*(1 - x - x^2 - 2*x^3 - 2*x^5 + 4*x^6 + 6*x^7 + 6*x^8 + 2*x^9)). - Colin Barker, Mar 22 2018

Example

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

Crossrefs

Cf. A297986.

Sequence in context: A270614 A011489 A093601 * A193780 A220260 A238901

Adjacent sequences: A297978 A297979 A297980 * A297982 A297983 A297984

Keyword

nonn

Author

R. H. Hardin, Jan 10 2018

Status

approved