A148428 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), (0, 1, 0), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 18, 63, 246, 966, 3945, 16467, 70342, 305616, 1346621, 6002092, 27002568, 122514743, 559932241, 2575770147, 11915970386, 55402390326, 258732896169, 1213120481918, 5708469495806, 26949628281003, 127606674587595, 605851015531093, 2883560007085763, 13755420395907659, 65754153711266080

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A241894 A148427 A068000 * A266833 A148429 A093635

Adjacent sequences: A148425 A148426 A148427 * A148429 A148430 A148431

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved