A150679 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), (0, 0, -1), (0, 0, 1), (0, 1, 1), (1, 1, -1)}.

1, 2, 8, 26, 112, 426, 1912, 7866, 36176, 155882, 728352, 3234762, 15281976, 69317882, 330139440, 1520823338, 7288057984, 33970036618, 163582528568, 769502319354, 3720050229648, 17628347473962, 85495965434304, 407574850543242, 1982014206226936, 9495536340996922, 46281342441841840, 222650026659854250

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[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: A150676 A150677 A150678 * A150680 A150681 A150682

Adjacent sequences: A150676 A150677 A150678 * A150680 A150681 A150682

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved