A150860 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, 0, 0), (0, -1, 1), (1, 0, 0), (1, 1, -1), (1, 1, 1)}

1, 2, 8, 32, 142, 648, 3023, 14303, 68375, 329159, 1594484, 7758744, 37897926, 185697956, 912232185, 4491049519, 22150504070, 109418279581, 541221305601, 2680131163126, 13285174449477, 65910406783303, 327241722243114, 1625818620413653, 8082218216483970, 40198975626753471, 200032499600646360

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150857 A150858 A150859 * A308368 A072243 A150861

Adjacent sequences: A150857 A150858 A150859 * A150861 A150862 A150863

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved