A149597 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, -1), (1, -1, 0), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 15, 59, 223, 971, 4017, 17717, 76441, 345973, 1538209, 7065229, 31973001, 148448869, 681356587, 3191805359, 14808199315, 69832629095, 326627084291, 1548697533807, 7293174165747, 34739862582079, 164508967210571, 786573165216815, 3741858188500235, 17949155044907391, 85725343541364431

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, k, -1 + n] + aux[1 + i, -1 + 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: A149594 A149595 A149596 * A149598 A149599 A149600

Adjacent sequences: A149594 A149595 A149596 * A149598 A149599 A149600

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved