A149436 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), (0, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 4, 13, 46, 170, 632, 2377, 9130, 35114, 135854, 530218, 2071864, 8120100, 31966534, 125949879, 497098272, 1966882682, 7787141436, 30862959230, 122506652958, 486488602742, 1933245169996, 7689973167922, 30598706621704, 121811086152620, 485235312497206, 1933403921250936

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, -1 + j, 1 + k, -1 + n] + aux[i, 1 + 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: A149434 A026641 A149435 * A087440 A149437 A149438

Adjacent sequences: A149433 A149434 A149435 * A149437 A149438 A149439

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved