A150368 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, 0), (1, -1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 94, 357, 1519, 6195, 26950, 114187, 504639, 2190082, 9791313, 43205127, 194850625, 870315396, 3951836163, 17815087768, 81338785555, 369345445042, 1694024296573, 7737230531213, 35623621507846, 163487185465527, 755195334127306, 3479713518316390, 16119455188080469, 74526182714110913

Offset

0,2

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, 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: A150365 A150366 A150367 * A150369 A150370 A150371

Adjacent sequences: A150365 A150366 A150367 * A150369 A150370 A150371

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved