A150939 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, 0), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 34, 158, 679, 3253, 14760, 71727, 335029, 1641681, 7805363, 38448803, 184950224, 914283364, 4433932897, 21973441964, 107194799250, 532196641059, 2607787106524, 12964687028927, 63744253779301, 317236969003621, 1563950103913332, 7789662614181180, 38484275002263516, 191804329393300946

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, 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: A150937 A150938 A151307 * A150940 A150941 A150942

Adjacent sequences: A150936 A150937 A150938 * A150940 A150941 A150942

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved