A150698 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, -1), (-1, 1, 0), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 26, 120, 445, 2124, 8376, 40551, 165818, 809755, 3391935, 16651254, 70961718, 349588037, 1509317512, 7454453718, 32513831916, 160886810618, 707534311251, 3506150369876, 15524265884075, 77018262334320, 342973029893813, 1703126092773058, 7621442565437130, 37875420909333996, 170210485307146438

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[1 + i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A150695 A150696 A150697 * A150699 A150700 A150701

Adjacent sequences: A150695 A150696 A150697 * A150699 A150700 A150701

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved