A150048 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), (0, 0, -1), (0, 0, 1), (0, 1, -1), (1, 0, 0)}.

1, 2, 6, 18, 61, 210, 775, 2880, 11167, 43450, 174162, 699434, 2871416, 11799186, 49318291, 206225105, 874196472, 3706064495, 15889015969, 68112992527, 294754698073, 1275221193581, 5561717925056, 24248871644687, 106464002206487, 467252246935953, 2063253080723396, 9107050843279229

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, j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 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: A150047 A386254 A393769 * A363511 A150049 A150050

Adjacent sequences: A150045 A150046 A150047 * A150049 A150050 A150051

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved