A149432 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), (-1, 1, 0), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 13, 45, 174, 710, 2829, 11685, 49826, 212370, 908756, 3967406, 17428452, 76575883, 339309966, 1515297265, 6775762236, 30392803463, 137107357008, 620274107946, 2810115185408, 12773447145043, 58242082395214, 265937635904625, 1216485786889994, 5578551230005231, 25624367940626478

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A189348 A165205 A149431 * A155397 A155328 A096353

Adjacent sequences: A149429 A149430 A149431 * A149433 A149434 A149435

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved