A148814 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, 0, 0), (0, -1, 0), (0, 0, 1), (0, 1, -1), (1, 1, -1)}.

1, 1, 3, 8, 26, 87, 308, 1129, 4258, 16401, 64399, 256816, 1037571, 4239492, 17496610, 72839052, 305557831, 1290667314, 5485660832, 23445450636, 100712243095, 434628533918, 1883622613990, 8195129117207, 35783068474745, 156763846451702, 688897134052493, 3036057675681138, 13416279582944950

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, 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: A148812 A148813 A369618 * A161938 A189177 A151444

Adjacent sequences: A148811 A148812 A148813 * A148815 A148816 A148817

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved