A295601 Number of n X 3 0..1 arrays with each 1 horizontally or vertically adjacent to 0, 2, 3 or 4 1s.

5, 20, 83, 338, 1425, 6080, 26249, 114298, 501405, 2211832, 9799095, 43554852, 194071913, 866357594, 3872915901, 17331341902, 77618369051, 347815345000, 1559266623743, 6992481752642, 31365036076887, 140713926545922

Offset

1,1

Comments

Column 3 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) = 7*a(n-1) - 9*a(n-2) - 11*a(n-3) + 14*a(n-4) - 53*a(n-5) + 19*a(n-6) + 42*a(n-7) - 23*a(n-8) + 72*a(n-9) + 36*a(n-10) - 25*a(n-11) - 12*a(n-12).

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

Example

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

Crossrefs

Cf. A295606.

Sequence in context: A030520 A183933 A323262 * A301946 A292760 A270322

Adjacent sequences: A295598 A295599 A295600 * A295602 A295603 A295604

Keyword

nonn

Author

R. H. Hardin, Nov 24 2017

Status

approved