A148935 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, 1), (-1, 1, 0), (0, 1, -1), (1, 0, 1)}.

1, 1, 3, 9, 28, 102, 361, 1335, 5190, 19890, 77799, 312792, 1250660, 5037901, 20652153, 84645208, 347614744, 1443123034, 6006612898, 25010222829, 104795484413, 440630256535, 1853405011001, 7823136808098, 33129247144801, 140408335939942, 596240121138146, 2538578287831345, 10820762924818603

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + 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: A151421 A148933 A148934 * A148936 A121656 A148937

Adjacent sequences: A148932 A148933 A148934 * A148936 A148937 A148938

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved