A196742 Number of n X 4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 2,3,1,0,4 for x=0,1,2,3,4.

1, 7, 71, 401, 2923, 19567, 134507, 919377, 6283897, 42987489, 293903925, 2009922151, 13744157339, 93985887721, 642701573055, 4394944856905, 30053778082923, 205515234410701, 1405365233289259, 9610242269541951

Offset

1,2

Comments

Every 0 is next to 0 2's, every 1 is next to 1 3, every 2 is next to 2 1's, every 3 is next to 3 0's, every 4 is next to 4 4's.

Column 4 of A196746.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Robert Israel, Maple-assisted proof of empirical formula

Formula

Empirical: a(n) = 3*a(n-1) + 26*a(n-2) + 16*a(n-3) - 99*a(n-4) + 2*a(n-5) + 81*a(n-6) - 330*a(n-7) + 340*a(n-8) - 212*a(n-9) + 124*a(n-10) + 81*a(n-11) - 30*a(n-12) + 5*a(n-13) - 3*a(n-14) - a(n-15).

Empirical formula verified: see link. - Robert Israel, Oct 06 2019

Example

Some solutions for n=5:
  0 0 3 0     0 0 0 0     0 3 0 0     0 0 3 0     0 0 0 0
  3 0 0 3     0 0 0 3     0 0 0 0     0 0 0 3     0 3 3 0
  0 3 1 0     3 0 1 0     0 3 0 3     0 3 1 0     0 0 0 3
  0 0 0 3     0 0 3 0     0 3 0 0     3 0 0 3     1 3 0 0
  0 3 0 0     0 3 0 0     0 0 0 0     0 0 3 0     0 0 0 0

Crossrefs

Sequence in context: A362106 A107601 A175863 * A196900 A319963 A198966

Adjacent sequences: A196739 A196740 A196741 * A196743 A196744 A196745

Keyword

nonn

Author

R. H. Hardin, Oct 06 2011

Status

approved