A264947 Number of 4 X n arrays containing n copies of 0..4-1 with no equal horizontal neighbors and new values introduced sequentially from 0.

1, 60, 3201, 184740, 11375145, 730983420, 48402531561, 3282992503164, 226854309720993, 15915758107113276, 1130694005695927761, 81177583723495750340, 5880587303767912833417, 429300706847441007321756

Offset

1,2

Comments

Row 4 of A264945.

Links

Christoph Koutschan, Table of n, a(n) for n = 1..80 (first 20 terms from R. H. Hardin).

M. Kauers and C. Koutschan, Some D-finite and some possibly D-finite sequences in the OEIS, arXiv:2303.02793 [cs.SC], 2023.

Example

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

Mathematica

cols = Tuples[{0, 1, 2, 3}, 4];
tmat = Table[If[Or @@ MapThread[SameQ, cols[[{i, j}]]], 0, 1], {i, 256}, {j, 256}];
vec = vvec = ((x^Count[#, 0] * y^Count[#, 1] * z^Count[#, 2]) & /@ cols);
Prepend[Table[vec = Expand[vvec*(tmat.vec)]; Coefficient[Total[vec], (x*y*z)^n]/24, {n, 2, 10}], 1]

Crossrefs

Cf. A264945.

Sequence in context: A084659 A230568 A180373 * A004297 A223657 A264369

Adjacent sequences: A264944 A264945 A264946 * A264948 A264949 A264950

Keyword

nonn

Author

R. H. Hardin, Nov 29 2015

Status

approved