A148582 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), (-1, 1, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 6, 20, 52, 180, 531, 1935, 6087, 23263, 76284, 302460, 1024293, 4164341, 14491325, 59869889, 213175734, 890626586, 3231206448, 13626322744, 50188107221, 213489198731, 796147909708, 3413510811070, 12866323062939, 55541100524599, 211337027327417, 917464966807871, 3520595766869871

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A151263 A148580 A148581 * A148583 A148584 A148585

Adjacent sequences: A148579 A148580 A148581 * A148583 A148584 A148585

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved