A150754 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, 0), (1, 0, 1), (1, 1, -1), (1, 1, 0)}

1, 2, 8, 29, 129, 535, 2481, 10920, 51623, 234730, 1122285, 5207410, 25086020, 118006138, 571525224, 2715031975, 13201588382, 63175979381, 308125926722, 1482898802721, 7250043605165, 35048497277894, 171694388326633, 833025387665248, 4087498427245526, 19890913275806299, 97736369540950671

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + 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, 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: A150753 A162066 A151302 * A150755 A150756 A150757

Adjacent sequences: A150751 A150752 A150753 * A150755 A150756 A150757

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved