A148413 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, 0), (0, 1, 0), (1, -1, 1), (1, 0, -1)}.

1, 1, 2, 5, 17, 59, 209, 783, 2969, 11818, 48041, 197875, 829325, 3504606, 15030624, 65140862, 284465160, 1252897588, 5548473208, 24743623447, 110991861676, 500241513919, 2265903803712, 10302193469158, 47033998962322, 215522897042267, 990747858248266, 4569280467583454, 21129681319052978

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 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: A056679 A084528 A149993 * A149994 A149995 A149996

Adjacent sequences: A148410 A148411 A148412 * A148414 A148415 A148416

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved