A296683 Number of n X 3 0..1 arrays with each 1 adjacent to 1, 2 or 3 king-move neighboring 1s.

4, 43, 210, 1162, 6959, 39608, 226599, 1305725, 7497482, 43051551, 247361324, 1420935204, 8162170909, 46887717710, 269343435641, 1547219822419, 8887903925214, 51055949141455, 293287243303968, 1684768052870030

Offset

1,1

Comments

Column 3 of A296688.

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = 4*a(n-1) + 4*a(n-2) + 37*a(n-3) - 15*a(n-4) + 21*a(n-5) - 79*a(n-6) - 7*a(n-7) - 92*a(n-8) - 49*a(n-9) - 19*a(n-10) - 20*a(n-11) + 2*a(n-12).

Empirical formula verified by Robert Israel, Dec 18 2017: see link.

Example

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

Crossrefs

Cf. A296688.

Sequence in context: A200000 A198209 A220774 * A297649 A186678 A186768

Adjacent sequences: A296680 A296681 A296682 * A296684 A296685 A296686

Keyword

nonn

Author

R. H. Hardin, Dec 18 2017

Status

approved