A148695 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, 0), (0, 0, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 7, 23, 68, 238, 808, 2938, 10616, 40028, 151564, 586471, 2283160, 9027376, 35968594, 144723618, 585936607, 2390988241, 9817042075, 40548235574, 168289941614, 701951164497, 2941244446309, 12376091360723, 52267911299832, 221529445747065, 942115413840111, 4019368944366612

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A096019 A148693 A148694 * A148696 A148697 A148698

Adjacent sequences: A148692 A148693 A148694 * A148696 A148697 A148698

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved