A148917 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), (1, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 8, 33, 119, 542, 2233, 10559, 46516, 224322, 1026708, 5008409, 23474135, 115329173, 549092258, 2710308246, 13044957193, 64594204771, 313331706590, 1554978664229, 7586468922828, 37710357210711, 184788064900446, 919631032698889, 4521633561970373, 22523025176604767, 111036257919281416

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[-1 + 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: A284963 A372642 A148916 * A120892 A195499 A225688

Adjacent sequences: A148914 A148915 A148916 * A148918 A148919 A148920

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved