A148523 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, 0, 1), (1, 1, 0)}.

1, 1, 3, 5, 19, 39, 145, 321, 1255, 2963, 11461, 27917, 110259, 277159, 1087913, 2782553, 11042671, 28776715, 113756413, 299773221, 1192805707, 3182466959, 12629930193, 33962881873, 135354541927, 367196191059, 1460721651845, 3985972843421, 15901830280195, 43678504771607, 174021430400217, 480174205835977

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[1 + i, j, -1 + 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: A128027 A128066 A273020 * A148524 A148525 A148526

Adjacent sequences: A148520 A148521 A148522 * A148524 A148525 A148526

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved