A148226 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, -1), (0, 0, 1), (1, -1, -1), (1, 1, -1)}.

1, 1, 2, 4, 13, 31, 99, 301, 1027, 3231, 11284, 39376, 138731, 489955, 1797810, 6590166, 24181127, 90210217, 341039892, 1285487504, 4878883689, 18749626333, 72233814243, 278434319785, 1082555277221, 4233318275461, 16554431903760, 64994452831710, 256794654265047, 1016252913256697, 4027029604504145

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A148223 A148224 A148225 * A004644 A000866 A320424

Adjacent sequences: A148223 A148224 A148225 * A148227 A148228 A148229

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved