A149372 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), (-1, 0, 1), (0, 1, -1), (1, -1, 0), (1, 1, 0)}.

1, 1, 4, 12, 46, 163, 664, 2674, 11203, 47344, 204884, 896034, 3961142, 17675669, 79602985, 360846935, 1645807487, 7549642897, 34808756325, 161175927217, 749252331727, 3496118882202, 16366958873973, 76846533998919, 361816051798841, 1707923275669555, 8080788170916935, 38314956899578467

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A027288 A149370 A149371 * A126202 A149373 A259203

Adjacent sequences: A149369 A149370 A149371 * A149373 A149374 A149375

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved