A150452 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, 1), (-1, 1, 1), (1, 0, 0), (1, 1, -1), (1, 1, 0)}.

1, 2, 7, 24, 105, 425, 1977, 8631, 41261, 187676, 910559, 4246915, 20787681, 98571981, 485219638, 2327411883, 11500348994, 55622208284, 275578607198, 1341114592732, 6657370299054, 32551554792627, 161820037945969, 794141060496540, 3952133603604302, 19451910424970058, 96886232243443329

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, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A150449 A150450 A150451 * A330254 A375129 A330506

Adjacent sequences: A150449 A150450 A150451 * A150453 A150454 A150455

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved