A149513 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), (1, -1, -1), (1, 1, 1)}.

1, 1, 5, 11, 47, 155, 601, 2255, 8981, 34599, 141187, 561435, 2304911, 9360735, 38838245, 159466743, 667227123, 2769683191, 11647989101, 48731215829, 206061404939, 867147480815, 3682148906021, 15580433317623, 66380446504309, 282052095021781, 1205576096388165, 5140839868168313

Offset

0,3

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, -1 + k, -1 + n] + aux[-1 + 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: A149510 A149511 A149512 * A327494 A097743 A350648

Adjacent sequences: A149510 A149511 A149512 * A149514 A149515 A149516

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved