A148734 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, 0, 1)}.

1, 1, 3, 7, 25, 79, 289, 939, 3879, 13721, 56351, 204359, 876107, 3363515, 14276417, 54939611, 242275331, 961373425, 4204643455, 16739963681, 74880644565, 306101300517, 1356632692427, 5536347760371, 25067683115747, 104123064107999, 467830369531279, 1941607402967179, 8857249161728419

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[-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: A130463 A148733 A392205 * A124425 A321606 A118398

Adjacent sequences: A148731 A148732 A148733 * A148735 A148736 A148737

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved