A295939 Number of n X 4 0..1 arrays with each 1 adjacent to 1 or 3 king-move neighboring 1's.

4, 33, 120, 534, 2976, 13759, 65009, 325008, 1565481, 7539236, 36795842, 178342390, 863486059, 4193371665, 20339714386, 98614688025, 478433693926, 2320695414662, 11255335524904, 54595627967873, 264817091402701, 1284455883761926

Offset

1,1

Comments

Column 4 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) = 2*a(n-1) + 5*a(n-2) + 52*a(n-3) - 12*a(n-4) - 55*a(n-5) - 505*a(n-6) - 34*a(n-7) - 70*a(n-8) + 1673*a(n-9) + 259*a(n-10) + 938*a(n-11) - 1632*a(n-12) + 663*a(n-13) - 899*a(n-14) + 985*a(n-15) - 542*a(n-16) + 19*a(n-17) + 89*a(n-18) - 104*a(n-19) + 7*a(n-20) - 14*a(n-21).

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

Example

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

Crossrefs

Cf. A295943.

Sequence in context: A133630 A279866 A066645 * A297515 A027169 A152041

Adjacent sequences: A295936 A295937 A295938 * A295940 A295941 A295942

Keyword

nonn

Author

R. H. Hardin, Nov 30 2017

Status

approved