A148646 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), (-1, 1, 1), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 6, 23, 62, 262, 812, 3573, 12012, 54270, 193053, 888926, 3295073, 15374504, 58782452, 276979000, 1085072796, 5152041461, 20583672366, 98328543277, 399250355193, 1916609557545, 7888286150870, 38021519436246, 158300490287993, 765598638786988, 3219300356467260, 15614479279145606

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A240646 A148644 A148645 * A148647 A148648 A013213

Adjacent sequences: A148643 A148644 A148645 * A148647 A148648 A148649

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved