A299309 Number of nX3 0..1 arrays with every element equal to 1, 2, 4, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 7, 15, 29, 63, 199, 593, 1657, 4689, 13395, 38357, 109855, 313667, 896417, 2563517, 7330205, 20956899, 59914557, 171302635, 489779503, 1400327457, 4003663145, 11446878297, 32727841823, 93572301793, 267532776375, 764903730599

Offset

1,2

Comments

Column 3 of A299314.

Links

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

Formula

Empirical: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) -3*a(n-4) -6*a(n-5) -8*a(n-6) +18*a(n-7) +27*a(n-8) -18*a(n-9) +15*a(n-10) -55*a(n-11) +21*a(n-12) -6*a(n-13) +14*a(n-14) +2*a(n-15) -2*a(n-16) for n>17

Example

Some solutions for n=6
..0..1..1. .0..1..0. .0..1..0. .0..1..0. .0..1..0. .0..1..1. .0..1..1
..0..0..1. .1..0..0. .1..0..1. .0..1..0. .0..0..1. .0..0..1. .0..0..1
..0..0..0. .0..0..0. .0..0..0. .1..1..1. .0..0..0. .0..0..0. .0..0..0
..0..0..0. .0..0..0. .0..0..0. .1..1..1. .0..0..0. .0..0..0. .0..0..0
..1..0..1. .1..0..1. .0..0..1. .1..1..0. .1..0..0. .1..0..0. .0..0..1
..1..0..1. .0..1..0. .0..1..0. .1..0..0. .0..1..0. .0..1..0. .0..1..1

Crossrefs

Cf. A299314.

Sequence in context: A198589 A298391 A299509 * A300110 A139597 A210675

Adjacent sequences: A299306 A299307 A299308 * A299310 A299311 A299312

Keyword

nonn

Author

R. H. Hardin, Feb 06 2018

Status

approved