A299137 Number of n X 3 0..1 arrays with every element equal to 1, 2, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

1, 18, 129, 899, 6205, 43066, 298361, 2068149, 14334327, 99354814, 688646455, 4773147461, 33083623049, 229309139316, 1589386941041, 11016355018433, 76356533603993, 529242224053012, 3668282443014641, 25425590535640541

Offset

1,2

Comments

Column 3 of A299142.

Links

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

Formula

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

Empirical g.f.: x*(1 + 12*x + 13*x^2 - 7*x^3 - 13*x^4 + 41*x^5 - 41*x^6 - 106*x^7 - 37*x^8 + 14*x^9 + 2*x^10) / ((1 - x)*(1 - 5*x - 13*x^2 - x^3 - 9*x^4 - 16*x^5 - 12*x^6 - 10*x^7 - 3*x^8 + 2*x^9)). - Colin Barker, Feb 17 2018

Example

Some solutions for n=5:
..0..0..1. .0..0..0. .0..1..1. .0..1..1. .0..0..1. .0..1..1. .0..0..1
..1..0..1. .0..1..0. .0..1..0. .0..0..1. .1..1..0. .1..0..0. .0..0..1
..1..1..0. .0..0..1. .0..1..0. .1..0..0. .0..0..1. .0..1..1. .1..0..1
..1..0..0. .1..1..0. .0..0..0. .1..0..1. .0..1..0. .0..0..1. .0..1..0
..0..1..1. .1..0..1. .0..0..0. .1..1..0. .1..0..1. .1..1..1. .1..0..0

Crossrefs

Cf. A299142.

Sequence in context: A244879 A142965 A298275 * A299368 A299932 A058649

Adjacent sequences: A299134 A299135 A299136 * A299138 A299139 A299140

Keyword

nonn

Author

R. H. Hardin, Feb 03 2018

Status

approved