A149219 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, -1, 1), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 10, 42, 145, 617, 2418, 10527, 43798, 195143, 841025, 3814325, 16840580, 77360042, 347761521, 1612823330, 7351384114, 34353120607, 158284028430, 744310087644, 3459062907239, 16351347409907, 76526100802650, 363350337600870, 1710519792567583, 8152301038474579, 38568972827017127

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + 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: A149216 A149217 A149218 * A361938 A222475 A194993

Adjacent sequences: A149216 A149217 A149218 * A149220 A149221 A149222

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved