A149147 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, 1), (-1, 1, -1), (1, 0, -1), (1, 0, 1)}.

1, 1, 4, 9, 38, 111, 477, 1593, 6954, 25101, 111245, 421669, 1895942, 7424769, 33816664, 135567201, 624118470, 2547578027, 11830222149, 48999526377, 229130337164, 960584070247, 4517804622196, 19133276961661, 90428499614550, 386287368914329, 1833395676854963, 7890147722387035, 37584984231943110

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A249101 A289157 A149146 * A149148 A149149 A149150

Adjacent sequences: A149144 A149145 A149146 * A149148 A149149 A149150

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved