A148409 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, 1, 0), (0, 0, -1), (0, 1, 0), (1, -1, 1)}.

1, 1, 2, 5, 17, 55, 187, 664, 2461, 9313, 36036, 141602, 564987, 2283709, 9329500, 38470803, 160040669, 670687191, 2829541104, 12011760502, 51268044607, 219910158631, 947691098759, 4100976732537, 17814653461222, 77667474546123, 339722451294319, 1490525565318239, 6558618691242851

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[i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A191640 A148408 A002692 * A149980 A149981 A149982

Adjacent sequences: A148406 A148407 A148408 * A148410 A148411 A148412

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved