A149406 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, 0, 1), (-1, 1, 1), (1, -1, 0), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 12, 52, 190, 850, 3433, 15725, 67088, 312593, 1379704, 6507124, 29391737, 139840831, 642273010, 3075896765, 14305813433, 68859801542, 323395442425, 1562939548509, 7397157690171, 35867819722084, 170821813960206, 830563578845814, 3976006093325299, 19376694311869116, 93158191980353477

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + i, 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, j, -1 + 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: A127866 A149404 A149405 * A149407 A149408 A125529

Adjacent sequences: A149403 A149404 A149405 * A149407 A149408 A149409

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved