A150809 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, 1), (0, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 31, 134, 583, 2635, 12013, 55748, 260199, 1225770, 5807958, 27657154, 132253448, 634831120, 3056093296, 14753704520, 71388767851, 346141434992, 1681478734536, 8181385374089, 39865926681487, 194517707470655, 950230680229559, 4647053166716503, 22748803560770153, 111463635930088743

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + 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: A150806 A150807 A150808 * A150810 A150811 A150812

Adjacent sequences: A150806 A150807 A150808 * A150810 A150811 A150812

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved