A150815 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, 0, 1), (1, 1, 0)}

1, 2, 8, 31, 135, 595, 2717, 12528, 58626, 276350, 1312487, 6264541, 30039360, 144544510, 697680731, 3376089128, 16373450997, 79560030026, 387242778625, 1887626066821, 9213486365027, 45024232130827, 220258651592205, 1078549091994023, 5286031993647663, 25928049502830068, 127271635056474974

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, k, -1 + n] + aux[-1 + i, 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: A150812 A150813 A150814 * A150816 A150817 A150818

Adjacent sequences: A150812 A150813 A150814 * A150816 A150817 A150818

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved