A149965 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, 0, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 16, 54, 193, 726, 2808, 11132, 45078, 185477, 773541, 3264268, 13912595, 59806475, 259038190, 1129476172, 4953975376, 21843387803, 96772415696, 430576585593, 1923275316368, 8621383283982, 38772924750758, 174896260712004, 791098631291058, 3587481422361201, 16307125392471257

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, 1 + 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: A149963 A149964 A148399 * A149966 A149967 A148400

Adjacent sequences: A149962 A149963 A149964 * A149966 A149967 A149968

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved