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

0,2

Links

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

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

Example

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

Crossrefs

Column 4 of A297595.

Sequence in context: A149448 A149449 A149450 * A294298 A300579 A180007

Adjacent sequences: A297588 A297589 A297590 * A297592 A297593 A297594

Keyword

nonn

Author

R. H. Hardin, Jan 01 2018

Extensions

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

Status

approved