A297591 Number of n X 4 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 5 neighboring 1s.

1, 4, 13, 49, 154, 577, 1977, 6962, 24441, 85803, 300758, 1056231, 3705161, 13002296, 45626359, 160104845, 561810578, 1971441799, 6917860901, 24275155066, 85182802525, 298910850927, 1048893665520, 3680622917741, 12915496721997, 45321151308320, 159034280809195

Offset: 0

Author

R. H. Hardin, Jan 01 2018

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000 (terms n = 1..210 from R. H. Hardin)

Crossrefs

Column 4 of A297595.

Formula

Empirical: a(n) = a(n-1) + 6*a(n-2) + 10*a(n-3) + 3*a(n-4) - 13*a(n-5) + 3*a(n-6) - 3*a(n-7) - 4*a(n-8) - a(n-9).

Empirical g.f.: 1 + x*(4 + 9*x + 12*x^2 - 13*x^3 - 13*x^4 - x^5 - 7*x^6 - 5*x^7 - x^8) / (1 - x - 6*x^2 - 10*x^3 - 3*x^4 + 13*x^5 - 3*x^6 + 3*x^7 + 4*x^8 + x^9). - Colin Barker, Mar 01 2019

Extensions

a(0)=1 prepended by Alois P. Heinz, Mar 01 2019