A148680 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), (-1, 1, 0), (0, 0, -1), (1, 0, 1)}.

1, 1, 3, 7, 21, 73, 245, 793, 2815, 10075, 36727, 137411, 511099, 1902023, 7265539, 27944559, 107626613, 418427913, 1633245101, 6388652625, 25192946761, 99781420877, 395823365473, 1577503839685, 6310009049517, 25281085381601, 101614792870501, 409704814929945, 1654942675306197

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A372649 A148678 A148679 * A001576 A169587 A075211

Adjacent sequences: A148677 A148678 A148679 * A148681 A148682 A148683

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved