A296110 Number of n X 3 0..1 arrays with each 1 adjacent to 3 or 4 king-move neighboring 1's.

1, 3, 6, 9, 26, 74, 163, 535, 1735, 4960, 15935, 51598, 159682, 507871, 1626269, 5134567, 16304686, 51939793, 164789906, 523362014, 1664172607, 5285951875, 16791701819, 53363480620, 169541243631, 538639046154, 1711496670766

Offset

1,2

Comments

Column 3 of A296115.

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = a(n-1) +3*a(n-2) +15*a(n-3) +2*a(n-4) -18*a(n-5) -36*a(n-6) -21*a(n-7) -25*a(n-8) +3*a(n-9) +11*a(n-10) +6*a(n-11).

Empirical formula verified by Robert Israel, Dec 04 2017 (see link).

Example

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

Crossrefs

Cf. A296115.

Sequence in context: A318032 A326160 A301536 * A019461 A223556 A067862

Adjacent sequences: A296107 A296108 A296109 * A296111 A296112 A296113

Keyword

nonn

Author

R. H. Hardin, Dec 04 2017

Status

approved