A148590 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, 1), (0, 0, 1), (0, 1, -1), (1, 0, -1)}.

1, 1, 3, 6, 20, 55, 206, 654, 2563, 8800, 35718, 130207, 541770, 2054906, 8698409, 34033759, 146141882, 585604786, 2541893678, 10381735748, 45477053043, 188672305570, 832663144479, 3499532437359, 15543200005075, 66047435923869, 294951865746390, 1265127279872257, 5676545403285557

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, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A186409 A148588 A148589 * A363592 A148591 A148592

Adjacent sequences: A148587 A148588 A148589 * A148591 A148592 A148593

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved