A148535 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, -1, 0), (-1, 1, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 3, 5, 19, 45, 161, 437, 1597, 4979, 17731, 58043, 211817, 731315, 2667389, 9354133, 34895869, 125833675, 470388199, 1710015661, 6496866717, 24060085297, 91545064515, 340787297207, 1312328307121, 4950750012475, 19084524663487, 72256609926249, 281126285543083, 1075206057955317, 4186271712634347

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A133603 A201867 A148534 * A148536 A148537 A148538

Adjacent sequences: A148532 A148533 A148534 * A148536 A148537 A148538

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved