A148482 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, 1), (-1, 1, 0), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 6, 20, 75, 292, 1170, 4851, 20563, 89106, 392367, 1751226, 7905810, 36027971, 165554708, 766145002, 3567650698, 16703779512, 78583666074, 371279300826, 1760834565971, 8379438799419, 39998229564078, 191455464627359, 918719826472986, 4418636543517328, 21295915716871996, 102832480619165634

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[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150163 A150164 A150165 * A148483 A150166 A150167

Adjacent sequences: A148479 A148480 A148481 * A148483 A148484 A148485

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved