A150609 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, 0, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 27, 111, 474, 2081, 9331, 42489, 195793, 910692, 4268460, 20134127, 95477700, 454802895, 2174770738, 10433966295, 50205026645, 242188473956, 1170953745475, 5672804595144, 27531900590553, 133837053812043, 651554256083783, 3176142708313533, 15501485931109490, 75740052339683311

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, 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: A150606 A150607 A150608 * A150610 A150611 A150612

Adjacent sequences: A150606 A150607 A150608 * A150610 A150611 A150612

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved