A245865 Number of length n+2 0..4 arrays with some pair in every consecutive three terms totalling exactly 4.

61, 193, 549, 1629, 4753, 13961, 40901, 119953, 351649, 1031057, 3022933, 8863117, 25986061, 76189749, 223384017, 654949861, 1920277409, 5630150189, 16507298221, 48398515249, 141901859897, 416048676085, 1219832512513, 3576483842281

Offset

1,1

Links

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

Formula

Empirical: a(n) = 3*a(n-1) + a(n-2) - a(n-3) - 5*a(n-4) - 8*a(n-5) + 3*a(n-6).

Empirical g.f.: x*(61 + 10*x - 91*x^2 - 150*x^3 - 185*x^4 + 75*x^5) / (1 - 3*x - x^2 + x^3 + 5*x^4 + 8*x^5 - 3*x^6). - Colin Barker, Nov 04 2018

Example

Some solutions for n=8:
  1   1   0   4   1   3   2   0   0   0   1   4   2   2   1   3
  2   4   1   1   0   0   2   1   2   4   0   0   3   2   3   0
  3   0   3   3   4   4   0   3   2   4   3   1   1   0   1   4
  2   4   1   0   3   0   4   1   1   0   1   4   2   4   2   2
  2   4   1   4   1   3   2   2   2   4   1   0   3   0   2   2
  0   0   3   0   3   1   2   2   3   2   3   3   1   1   2   0
  2   4   3   4   2   0   0   4   1   2   4   1   0   3   2   4
  2   3   1   0   1   3   2   0   3   1   0   4   4   1   4   3
  0   1   3   4   2   1   2   2   4   3   1   0   0   4   0   0
  2   4   1   3   2   3   4   2   1   3   4   1   1   0   4   1

Crossrefs

Column 4 of A245869.

Sequence in context: A121513 A139508 A364716 * A357780 A259410 A234925

Adjacent sequences: A245862 A245863 A245864 * A245866 A245867 A245868

Keyword

nonn

Author

R. H. Hardin, Aug 04 2014

Status

approved