A295938 Number of n X 3 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1's.

3, 15, 41, 120, 465, 1472, 4667, 16230, 53266, 173851, 584543, 1934414, 6378634, 21232506, 70378723, 232896476, 772967540, 2562676394, 8490559710, 28155930393, 93345299815, 309390211243, 1025742299033, 3400526966741, 11272379148340

Offset

1,1

Comments

Column 3 of A295943.

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) + 18*a(n-3) + a(n-4) - 19*a(n-5) - 36*a(n-6) - 13*a(n-7) + 5*a(n-8) + 10*a(n-9).

Empirical formula confirmed by Robert Israel, Nov 30 2017 (see link).

Example

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

Crossrefs

Cf. A295943.

Sequence in context: A298655 A299608 A249835 * A096742 A012256 A012222

Adjacent sequences: A295935 A295936 A295937 * A295939 A295940 A295941

Keyword

nonn

Author

R. H. Hardin, Nov 30 2017

Status

approved