A150385 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, -1, 0), (-1, 1, 0), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 98, 361, 1641, 6456, 29975, 122797, 578538, 2430398, 11586047, 49532072, 238059400, 1031522751, 4985820454, 21833680533, 105999201265, 468105465078, 2280838830949, 10141757366336, 49561550196373, 221645646042901, 1085765734275864, 4879481984566974, 23951166794986119, 108090536459660901

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A150382 A150383 A150384 * A047066 A150386 A150387

Adjacent sequences: A150382 A150383 A150384 * A150386 A150387 A150388

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved