A149026 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, 1, -1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 9, 39, 137, 623, 2441, 11359, 47521, 224359, 977861, 4663291, 20889033, 100338007, 458283489, 2213130847, 10255221601, 49728217447, 232997035357, 1133494314963, 5357336598661, 26131321902595, 124372530000641, 607970318813431, 2910173855944909, 14251859249211531, 68541473702526857

Offset

0,3

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, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A059804 A065657 A296102 * A149027 A330795 A180741

Adjacent sequences: A149023 A149024 A149025 * A149027 A149028 A149029

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved