A296015 Number of n X 4 0..1 arrays with each 1 adjacent to 1 or 4 king-move neighboring 1s.

4, 28, 91, 366, 1644, 6545, 26865, 112345, 461363, 1902251, 7867396, 32451301, 133919803, 552939041, 2282127828, 9419468870, 38881999590, 160489339983, 662439317422, 2734335195143, 11286359484536, 46586079223617

Offset

1,1

Comments

Column 4 of A296019.

Links

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

Robert Israel, Maple-assisted proof of formula

Formula

Empirical: a(n) = a(n-1) + 6*a(n-2) + 36*a(n-3) + 8*a(n-4) - 71*a(n-5) - 345*a(n-6) - 221*a(n-7) + 167*a(n-8) + 1167*a(n-9) + 930*a(n-10) + 200*a(n-11) - 1607*a(n-12) - 1327*a(n-13) - 670*a(n-14) + 1036*a(n-15) + 741*a(n-16) + 514*a(n-17) - 306*a(n-18) - 128*a(n-19) - 114*a(n-20) + 40*a(n-21).

Empirical formula confirmed by Robert Israel, Dec 03 2017 (see link).

Example

Some solutions for n=5:
  0 0 1 1    0 0 0 0    1 0 1 1    1 0 0 1    0 0 1 0
  0 0 0 0    1 0 1 1    1 0 0 0    0 1 1 0    0 0 0 1
  0 1 0 1    1 0 0 0    0 0 0 0    0 1 1 0    0 0 0 0
  1 0 0 1    0 0 0 0    0 0 1 0    0 1 0 0    0 0 1 0
  0 0 0 0    0 1 1 0    0 0 0 1    1 0 1 0    0 0 0 1

Crossrefs

Cf. A296019.

Sequence in context: A183437 A294315 A263239 * A187452 A173296 A077595

Adjacent sequences: A296012 A296013 A296014 * A296016 A296017 A296018

Keyword

nonn

Author

R. H. Hardin, Dec 02 2017

Status

approved