A231636 Number of n X 2 0..2 arrays with no element having a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors equal to itself plus one mod 3, with upper left element zero (rock paper and scissors drawn positions).

1, 5, 25, 124, 599, 2907, 14098, 68345, 331411, 1606976, 7792087, 37783439, 183209634, 888373029, 4307670407, 20887647824, 101283014043, 491115562211, 2381391364586, 11547230982705, 55991864805211, 271501360719136

Offset

1,2

Links

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

Formula

Empirical: a(n) = 7*a(n-1) - 11*a(n-2) + 4*a(n-3) - 14*a(n-4) + 48*a(n-5) - 48*a(n-6) + 16*a(n-7).

Empirical g.f.: x*(1 - x)^2 / (1 - 7*x + 11*x^2 - 4*x^3 + 14*x^4 - 48*x^5 + 48*x^6 - 16*x^7). - Colin Barker, Sep 29 2018

Example

Some solutions for n=7:
  0 1   0 0   0 0   0 1   0 1   0 0   0 0   0 1   0 0   0 0
  0 0   1 0   0 1   2 0   0 2   1 0   0 1   0 0   0 1   2 2
  1 0   1 0   1 2   2 2   1 2   2 1   0 1   1 0   1 2   2 2
  1 2   0 0   1 2   0 2   0 1   0 2   0 2   1 0   0 2   2 0
  1 1   0 1   0 1   2 0   0 0   2 0   2 2   2 2   2 1   2 0
  0 2   1 2   2 0   1 2   2 1   1 1   0 2   2 2   1 1   1 2
  2 2   1 1   2 2   1 1   1 1   2 1   0 1   2 0   2 1   1 1

Crossrefs

Column 2 of A231641.

Sequence in context: A278282 A086093 A171279 * A099504 A299958 A036156

Adjacent sequences: A231633 A231634 A231635 * A231637 A231638 A231639

Keyword

nonn

Author

R. H. Hardin, Nov 12 2013

Status

approved