A149696 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, 1), (0, 0, -1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 69, 249, 1117, 4529, 19893, 82313, 373677, 1609825, 7263205, 31601529, 144929117, 643356881, 2943504405, 13142716521, 60720099853, 274355968577, 1266272052037, 5743409115225, 26680362529213, 121961107159217, 566334183070581, 2595856470100297, 12109569624436333, 55810461563660321

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A149695 A162270 A146790 * A096980 A339684 A149697

Adjacent sequences: A149693 A149694 A149695 * A149697 A149698 A149699

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved