A148193 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, 1), (-1, 0, 1), (0, 0, -1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 4, 12, 32, 96, 297, 992, 3292, 11286, 39642, 142702, 517764, 1905053, 7112962, 26884881, 102419779, 393417205, 1524886160, 5956755229, 23413733787, 92563423743, 368132782768, 1472188208590, 5915511687809, 23873104348995, 96758275748263, 393773394807477, 1608501101799055, 6592904143659730

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A087211 A161177 A039721 * A341344 A002528 A216818

Adjacent sequences: A148190 A148191 A148192 * A148194 A148195 A148196

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved