A150641 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, 0, 1), (0, 1, 0), (1, 1, -1), (1, 1, 1)}.

1, 2, 7, 27, 117, 514, 2327, 10642, 49357, 230744, 1087567, 5155525, 24567985, 117557404, 564554431, 2719378931, 13133588981, 63574966648, 308364056247, 1498342592035, 7291987338193, 35538167303224, 173419545231847, 847231084853706, 4143441713783393, 20283190601772934, 99378472344960367

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150639 A150640 A175934 * A150642 A150643 A150644

Adjacent sequences: A150638 A150639 A150640 * A150642 A150643 A150644

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved