A300091 Number of n X 3 0..1 arrays with every element equal to 0, 2, 3, 5, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 7, 7, 19, 35, 95, 225, 575, 1563, 4179, 11555, 32259, 90327, 255307, 723255, 2054259, 5847519, 16660707, 47512875, 135574255, 386984391, 1104913059, 3155268051, 9011441543, 25738758919, 73519704603, 210007895555, 599899095903

Offset

1,2

Comments

Column 3 of A300096.

Links

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

Formula

Empirical: a(n) = 5*a(n-1) -4*a(n-2) -8*a(n-3) -5*a(n-4) +35*a(n-5) -4*a(n-6) -26*a(n-7) -10*a(n-8) -2*a(n-9) -8*a(n-10) +88*a(n-11) +78*a(n-12) -176*a(n-13) -62*a(n-14) +40*a(n-15) +24*a(n-16) +52*a(n-17) -8*a(n-18) -8*a(n-19) for n > 20.

Example

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

Crossrefs

Cf. A300096.

Sequence in context: A053416 A213031 A299453 * A094248 A282828 A339722

Adjacent sequences: A300088 A300089 A300090 * A300092 A300093 A300094

Keyword

nonn

Author

R. H. Hardin, Feb 24 2018

Status

approved