A150363 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), (-1, 1, 1), (0, 0, -1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 23, 92, 360, 1515, 6394, 27766, 121701, 541389, 2427628, 10994962, 50085884, 229825960, 1059427008, 4909468718, 22840737450, 106677011512, 499928196409, 2349932755977, 11077508816333, 52349546603423, 247976809550402, 1177163181636024, 5599152334827215, 26681459217085335, 127359498900974016

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, -1 + j, k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A150360 A150361 A150362 * A150364 A093636 A150365

Adjacent sequences: A150360 A150361 A150362 * A150364 A150365 A150366

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved