A149995 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, 1), (0, 1, 1), (1, 0, 0)}.

1, 2, 5, 17, 59, 214, 803, 3084, 12035, 47520, 190175, 767807, 3121485, 12777633, 52607949, 217615055, 903971491, 3770023829, 15776636920, 66218490239, 278713126944, 1176087850563, 4974012901260, 21080531329739, 89516666392125, 380805658516829, 1622622248429071, 6924695935436127

Offset

0,2

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, 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, 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: A149993 A148413 A149994 * A149996 A149997 A149998

Adjacent sequences: A149992 A149993 A149994 * A149996 A149997 A149998

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved