A149983 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), (0, -1, -1), (0, 0, 1), (1, 1, 0)}.

1, 2, 5, 17, 55, 200, 737, 2782, 10881, 42496, 171031, 688475, 2817527, 11609784, 48126841, 201562885, 845539099, 3580412372, 15187225367, 64821446779, 277615705565, 1192720740882, 5147664505465, 22251795763422, 96607920494837, 420046638765438, 1832258309887397, 8008819832696925

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[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: A149980 A149981 A149982 * A149984 A149985 A149986

Adjacent sequences: A149980 A149981 A149982 * A149984 A149985 A149986

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved