A149691 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), (0, 1, -1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 67, 271, 1163, 4975, 21989, 97645, 439891, 1996779, 9140657, 42072121, 194850683, 906555605, 4235833685, 19866026823, 93492032031, 441290511949, 2088700567263, 9910793319771, 47132758620649, 224615146747531, 1072480324073509, 5129843682085273, 24576984768779825, 117926903625905613

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[i, -1 + j, 1 + 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: A149688 A149689 A149690 * A149692 A149693 A149694

Adjacent sequences: A149688 A149689 A149690 * A149692 A149693 A149694

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved