A148497 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, 1), (-1, 1, 1), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 6, 22, 85, 355, 1492, 6556, 29052, 132014, 603615, 2800177, 13051694, 61391948, 289880238, 1377164008, 6563043266, 31411893330, 150726168692, 725525043255, 3499672398571, 16921628973465, 81962306917461, 397740786993856, 1932949695762718, 9407939072108970, 45846319524570560

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, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A150252 A150253 A150254 * A206736 A079105 A079104

Adjacent sequences: A148494 A148495 A148496 * A148498 A148499 A148500

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved