A148629 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), (-1, 1, 0), (1, -1, -1), (1, 0, 1)}.

1, 1, 3, 6, 22, 54, 212, 601, 2431, 7403, 30839, 98930, 419323, 1398966, 6002790, 20628864, 89480901, 314708612, 1376176233, 4934852427, 21722436519, 79144165263, 350386613557, 1293890741727, 5755579291231, 21502992065673, 96045126282623, 362451549275632, 1624794272142588, 6185991031287732

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + 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: A148626 A148627 A148628 * A151264 A148630 A148631

Adjacent sequences: A148626 A148627 A148628 * A148630 A148631 A148632

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved