A148964 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), (-1, 0, 1), (0, 0, -1), (0, 1, 1), (1, -1, 1)}

1, 1, 3, 9, 31, 105, 380, 1424, 5451, 21236, 84023, 336837, 1366529, 5597986, 23129943, 96272760, 403427906, 1701008029, 7211480972, 30724854989, 131497271065, 565125754561, 2438042909441, 10555465139832, 45849803838254, 199765279212025, 872844372120064, 3823935236078622, 16794571990271903

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A027096 A221440 A289599 * A148965 A130620 A202246

Adjacent sequences: A148961 A148962 A148963 * A148965 A148966 A148967

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved