A149661 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), (0, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 59, 239, 995, 3999, 16797, 72461, 311341, 1341853, 5899125, 26060865, 115032997, 511837889, 2294771479, 10295473175, 46310998767, 209480589415, 950055719843, 4313376010211, 19645164450867, 89742963487203, 410471846243603, 1880520192121503, 8636214371820259, 39724054861264127

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, j, 1 + k, -1 + n] + aux[i, -1 + 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: A149658 A149659 A149660 * A146130 A026619 A142956

Adjacent sequences: A149658 A149659 A149660 * A149662 A149663 A149664

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved