A149492 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, 0), (0, 1, 1), (1, -1, 0), (1, -1, 1), (1, 1, -1)}.

1, 1, 4, 14, 59, 243, 1065, 4708, 21395, 98025, 454964, 2126156, 10012574, 47398340, 225511507, 1077175891, 5163669175, 24827400812, 119693621775, 578392088330, 2800781899561, 13587499059804, 66027224835105, 321333792674211, 1565954585986436, 7640771328892362, 37323634647044161, 182506355382125949

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, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A360198 A296943 A104987 * A307488 A351634 A241706

Adjacent sequences: A149489 A149490 A149491 * A149493 A149494 A149495

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved