A148648 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), (-1, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 6, 23, 62, 269, 850, 3891, 13419, 62990, 229483, 1093201, 4139300, 19918865, 77643783, 376413282, 1501052044, 7317882715, 29721764794, 145523007631, 600006212256, 2947600993255, 12306920472227, 60619759341056, 255809804792113, 1262717951385575, 5377423110200973, 26589798486133635

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[1 + i, -1 + 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: A148645 A148646 A148647 * A013213 A013217 A013216

Adjacent sequences: A148645 A148646 A148647 * A148649 A148650 A148651

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved