A149079 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, 1, 1)}.

1, 1, 4, 7, 28, 70, 256, 763, 2764, 8566, 31632, 101426, 374720, 1246344, 4604448, 15560731, 57829276, 198086254, 737203600, 2563946970, 9548132880, 33486404056, 125061142552, 441810374578, 1651795298464, 5883706330624, 22010904801344, 78804288998592, 295307330346944, 1062095786177408, 3983244240356848

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[-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: A123767 A149077 A149078 * A149080 A366314 A176966

Adjacent sequences: A149076 A149077 A149078 * A149080 A149081 A149082

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved