A148401 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), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 17, 49, 175, 574, 2215, 7794, 31002, 114827, 469571, 1802223, 7507304, 29616634, 125224110, 504660980, 2158999665, 8852141829, 38237746911, 159011512866, 692421182858, 2913714414087, 12774870975808, 54299529666488, 239474510946361, 1026713175859252, 4551287121301993

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + 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: A051438 A376967 A368756 * A148402 A148403 A148404

Adjacent sequences: A148398 A148399 A148400 * A148402 A148403 A148404

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved