A150265 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, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 6, 22, 89, 340, 1436, 6161, 25845, 113360, 501973, 2188632, 9804450, 44168998, 196838674, 893243667, 4069331906, 18389008125, 84192537645, 386573832889, 1763865477474, 8128362192686, 37540320396029, 172512593472276, 798957493385075, 3706708734362354, 17127144863918236, 79635589447131234

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, -1 + k, -1 + n] + aux[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, 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: A294593 A214358 A107944 * A150266 A165522 A150267

Adjacent sequences: A150262 A150263 A150264 * A150266 A150267 A150268

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved