A150948 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, 1), (0, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 153, 673, 3056, 13961, 64691, 302034, 1419777, 6707589, 31848340, 151777512, 725705977, 3479885667, 16729718128, 80604358661, 389127748054, 1881938427809, 9116193100734, 44223103712110, 214814131463072, 1044728780081191, 5086579661859410, 24790977087846770, 120941239005789793

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, -1 + k, -1 + n] + aux[-1 + i, 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, 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: A150947 A110224 A363549 * A150949 A150950 A150951

Adjacent sequences: A150945 A150946 A150947 * A150949 A150950 A150951

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved