A149456 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, 1), (0, -1, 1), (0, 1, -1), (1, 0, 1)}.

1, 1, 4, 13, 50, 190, 782, 3215, 13641, 58212, 252802, 1103636, 4869562, 21584696, 96367184, 431885369, 1945585545, 8792673332, 39891459357, 181472254821, 828054203296, 3787075617322, 17362412411688, 79757374759960, 367118812101919, 1692704021049611, 7817930187182200, 36161426745654017

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, -1 + 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: A056275 A149455 A105968 * A149457 A149458 A364742

Adjacent sequences: A149453 A149454 A149455 * A149457 A149458 A149459

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved