A149647 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, 1), (-1, 1, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 15, 71, 247, 1201, 4519, 22269, 87991, 435723, 1777551, 8828245, 36823267, 183269901, 777183633, 3873252695, 16638290989, 82992609063, 360202691905, 1797817940981, 7868823634711, 39291800695933, 173187812119847, 865064459448701, 3835762742519765, 19163941326481269, 85410572339469807

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149644 A149645 A149646 * A149648 A149649 A149650

Adjacent sequences: A149644 A149645 A149646 * A149648 A149649 A149650

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved