A150637 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, 0, 0), (1, 1, -1)}.

1, 2, 7, 27, 115, 514, 2361, 11054, 52401, 250772, 1208727, 5859153, 28530895, 139443346, 683599043, 3359701039, 16546981423, 81641739090, 403427284767, 1996101954885, 9887495415811, 49024238960300, 243277490929813, 1208129816259934, 6003534144471875, 29850315257625048, 148494715878182467

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[-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: A150635 A150636 A084206 * A150638 A150639 A150640

Adjacent sequences: A150634 A150635 A150636 * A150638 A150639 A150640

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved