A149246 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, 0, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 4, 11, 38, 116, 440, 1453, 5450, 18714, 71816, 253494, 972292, 3492890, 13529192, 49328285, 191161466, 703792642, 2742710728, 10191899732, 39738557836, 148580923814, 581445525832, 2187826760962, 8565364278692, 32366865951050, 127044352702056, 482288980929490, 1893726046847320

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[1 + i, 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: A282702 A130494 A027573 * A149247 A149248 A149249

Adjacent sequences: A149243 A149244 A149245 * A149247 A149248 A149249

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved