A149448 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, 0, 1), (-1, 1, 0), (0, -1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 13, 48, 186, 753, 3097, 13053, 55769, 241140, 1053164, 4636881, 20557358, 91675021, 410927024, 1850129497, 8362763763, 37932271619, 172592759713, 787505869111, 3602359497451, 16516663397884, 75887948704330, 349351810417632, 1611113927635246, 7442244616664714, 34430542485823502

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[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A149446 A149447 A357642 * A149449 A149450 A297591

Adjacent sequences: A149445 A149446 A149447 * A149449 A149450 A149451

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved