A295602 Number of n X 4 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2, 3 or 4 1's.

8, 51, 338, 2305, 16340, 119371, 892086, 6775059, 52046892, 402986355, 3136847628, 24504233009, 191873294724, 1504755257129, 11813098224356, 92801573927465, 729356047596030, 5733901485086493, 45086207743916552, 354561409191514859

Offset

1,1

Comments

Column 4 of A295606.

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = 13*a(n-1) - 43*a(n-2) + 33*a(n-3) - 97*a(n-4) + 73*a(n-5) - 730*a(n-6) + 503*a(n-7) + 2269*a(n-8) + 2715*a(n-9) + 15348*a(n-10) + 11653*a(n-11) + 23118*a(n-12) + 14969*a(n-13) + 12525*a(n-14) - 73129*a(n-15) - 39381*a(n-16) + 23137*a(n-17) - 1963*a(n-18) + 10808*a(n-19) + 479*a(n-20) + 1751*a(n-21) + 102*a(n-22) + 5301*a(n-23) - 770*a(n-24) - 368*a(n-25) - 62*a(n-26) - 23*a(n-27).

Confirmed by Robert Israel, Nov 24 2017 (see link).

Example

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

Crossrefs

Cf. A295606.

Sequence in context: A014829 A048438 A348312 * A226199 A267637 A238648

Adjacent sequences: A295599 A295600 A295601 * A295603 A295604 A295605

Keyword

nonn

Author

R. H. Hardin, Nov 24 2017

Status

approved