A148554 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, -1, 0), (-1, 1, -1), (-1, 1, 0), (1, 0, 1)}.

1, 1, 3, 5, 23, 49, 203, 461, 2191, 5417, 24179, 61093, 294551, 778881, 3591867, 9589629, 46607903, 128126041, 601709315, 1661832149, 8118460327, 22893192881, 108762301515, 307387152813, 1507018386735, 4326952933769, 20721610011283, 59551484848901, 292725740699831, 851870785772257, 4103481872357339

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..600

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[1 + i, -1 + j, 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, 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: A280273 A036952 A065720 * A120937 A075307 A100302

Adjacent sequences: A148551 A148552 A148553 * A148555 A148556 A148557

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved