A149678 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, 0, 0), (1, 0, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 67, 247, 1099, 4455, 19465, 81113, 366871, 1581857, 7124697, 31095533, 142367227, 632488035, 2891693583, 12932761935, 59700835301, 269914718735, 1245367919345, 5654172178637, 26254857313453, 120070130409721, 557471773507155, 2556857793773571, 11925097576175443, 54978693493575749

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A062613 A153323 A059847 * A149679 A149680 A149681

Adjacent sequences: A149675 A149676 A149677 * A149679 A149680 A149681

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved