A150093 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, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, 0)}.

1, 2, 6, 19, 66, 246, 959, 3821, 15516, 64222, 269701, 1147397, 4920972, 21274085, 92683938, 406473019, 1792230903, 7938032686, 35313624670, 157740457577, 707180810177, 3180111103615, 14341410165138, 64853404230235, 294020538994255, 1336004749977621, 6083069299292362, 27751482911671438

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A150091 A190737 A150092 * A150094 A305118 A234010

Adjacent sequences: A150090 A150091 A150092 * A150094 A150095 A150096

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved