A299123 Number of n X 3 0..1 arrays with every element equal to 0, 1, 3, 4, 5 or 7 king-move adjacent elements, with upper left element zero.

3, 4, 9, 23, 31, 184, 427, 1115, 4128, 11024, 32827, 104959, 302093, 917104, 2804565, 8324555, 25231517, 76267810, 228857830, 691699768, 2085676297, 6280152762, 18952185100, 57128981249, 172189537544, 519305913429, 1565482526696

Offset

1,1

Comments

Column 3 of A299128.

Links

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

Formula

Empirical: a(n) = a(n-1) +4*a(n-2) +16*a(n-3) -13*a(n-4) -35*a(n-5) -62*a(n-6) +28*a(n-7) +65*a(n-8) +36*a(n-9) +61*a(n-10) +59*a(n-11) -34*a(n-12) -64*a(n-13) -36*a(n-14) -40*a(n-15) +3*a(n-16) +18*a(n-17) +2*a(n-18) for n>19.

Example

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

Crossrefs

Cf. A299128.

Sequence in context: A116868 A049976 A032789 * A245455 A296265 A034921

Adjacent sequences: A299120 A299121 A299122 * A299124 A299125 A299126

Keyword

nonn

Author

R. H. Hardin, Feb 03 2018

Status

approved