A149031 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, 1, 0), (0, 1, -1), (1, -1, 0), (1, 0, 1)}.

1, 1, 3, 10, 33, 127, 486, 1943, 8052, 33504, 143203, 618615, 2696818, 11919409, 52965105, 237386849, 1071312485, 4857376568, 22160738643, 101518175550, 467022106982, 2157328576831, 9996509638302, 46480743976377, 216739174880976, 1013326106030851, 4750067786683020, 22315803215975305

Offset

0,3

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149030 A024426 A326558 * A145928 A006535 A041633

Adjacent sequences: A149028 A149029 A149030 * A149032 A149033 A149034

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved