A150880 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, 0, 0), (0, 1, 1), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 8, 33, 148, 681, 3207, 15304, 73793, 358363, 1749904, 8580148, 42207338, 208156879, 1028695705, 5092223056, 25241971267, 125265601296, 622231878859, 3093281543257, 15387946642130, 76593647431680, 381434671792829, 1900349222963012, 9471261945540459, 47219646520069460, 235483534853526993

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150877 A150878 A150879 * A150881 A053817 A150882

Adjacent sequences: A150877 A150878 A150879 * A150881 A150882 A150883

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved