A150238 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, 0), (0, 0, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 6, 22, 83, 324, 1316, 5472, 23111, 98972, 428786, 1875110, 8264009, 36664072, 163605215, 733730362, 3305098457, 14945924693, 67821906606, 308723676681, 1409254511571, 6449317066818, 29583127079684, 135986054913807, 626309055038008, 2889750507675439, 13355195601933312, 61816693649394187

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A068946 A150237 A122449 * A150239 A150240 A150241

Adjacent sequences: A150235 A150236 A150237 * A150239 A150240 A150241

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved