A148725 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, 1), (-1, 0, 1), (0, 0, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 7, 25, 72, 278, 916, 3672, 12993, 53655, 199801, 841352, 3247398, 13885219, 55084307, 238324288, 965836929, 4218990574, 17394476665, 76585028175, 320237085936, 1419355904803, 6005418138172, 26768693800482, 114400021806862, 512438742183608, 2208901209753286, 9937017305427740

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A148724 A332508 A309911 * A148726 A148727 A148728

Adjacent sequences: A148722 A148723 A148724 * A148726 A148727 A148728

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved