A150946 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, 0), (0, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 151, 669, 3025, 13784, 63934, 298236, 1400365, 6616111, 31408939, 149615411, 715286089, 3429871086, 16486597064, 79426519820, 383442921843, 1854375708668, 8982371270559, 43574329625745, 211664278498859, 1029408823628497, 5012065403443161, 24428330224416733, 119174044389066286

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, 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: A289974 A289782 A150945 * A150947 A110224 A363549

Adjacent sequences: A150943 A150944 A150945 * A150947 A150948 A150949

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved