A149945 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), (0, 1, -1), (0, 1, 1), (1, 0, 0)}

1, 2, 5, 15, 50, 164, 572, 2007, 7147, 25744, 94470, 345562, 1283521, 4774425, 17870925, 67071406, 253596740, 957841394, 3641689270, 13852713872, 52882413683, 202064486221, 775138650253, 2972225528641, 11437906305874, 44025442187961, 169850215967115, 655535281281558, 2536205112396006

Offset

0,2

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + 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: A005751 A202182 A149944 * A149946 A149947 A149948

Adjacent sequences: A149942 A149943 A149944 * A149946 A149947 A149948

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved