A150592 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), (0, 0, -1), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 27, 105, 434, 1823, 7774, 33835, 148064, 654193, 2915791, 13048725, 58751884, 265691571, 1205496545, 5491102385, 25080469864, 114855451761, 527348708275, 2426105402995, 11184364852120, 51654525113001, 238941780810494, 1107044612289195, 5136168497982782, 23860240578462955, 110981370435242503

Offset

0,2

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, 1 + 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: A037381 A129013 A150591 * A150593 A024429 A136412

Adjacent sequences: A150589 A150590 A150591 * A150593 A150594 A150595

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved