A149571 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, -1), (-1, 1, 0), (1, -1, 0), (1, 1, 1)}

1, 1, 5, 13, 63, 203, 999, 3587, 17691, 67419, 333565, 1322809, 6556223, 26731127, 132674229, 552239801, 2743793869, 11604068827, 57702655875, 247148185971, 1229798067359, 5321999057913, 26496615787301, 115650961290621, 576055726075373, 2532553343278171, 12619514860678161, 55823435028402645

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, 1 + 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: A269514 A149569 A149570 * A149572 A149573 A149574

Adjacent sequences: A149568 A149569 A149570 * A149572 A149573 A149574

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved