A149342 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 0), (-1, 1, 0), (-1, 1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 12, 41, 155, 583, 2217, 8813, 35117, 140272, 571017, 2338774, 9587488, 39650883, 164907088, 686754386, 2872729884, 12067557814, 50778198371, 214221469713, 906453747063, 3842114215717, 16314537689999, 69423328905674, 295872508187261, 1262731872514009, 5397670645267912

Offset

0,3

Links

Table of n, a(n) for n=0..27.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A275184 A354338 A149341 * A149343 A225586 A242468

Adjacent sequences: A149339 A149340 A149341 * A149343 A149344 A149345

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved