A151142 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), (0, 1, 0), (1, 0, 0), (1, 1, 0)}

1, 3, 11, 47, 199, 887, 4007, 18295, 84839, 395159, 1856407, 8766263, 41568295, 198016663, 946007351, 4533908791, 21785184967, 104907997079, 506278355543, 2447542855991, 11852361301607, 57481586054295, 279149979077495, 1357365314039095, 6607645519512583, 32200121570335895, 157069431636977815

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, -1 + j, 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: A248208 A112567 A163063 * A151143 A151144 A151145

Adjacent sequences: A151139 A151140 A151141 * A151143 A151144 A151145

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved