A149150 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), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 9, 38, 111, 491, 1619, 7448, 26306, 123930, 459055, 2191280, 8408836, 40486937, 159582815, 773367694, 3112854417, 15160540050, 62063629949, 303427184699, 1259618217221, 6176936899574, 25944142838499, 127538542044858, 541041116351226, 2665083280305249, 11403091715885735, 56264553278451650

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, 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, -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: A149147 A149148 A149149 * A149151 A149152 A149153

Adjacent sequences: A149147 A149148 A149149 * A149151 A149152 A149153

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved