A148696 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), (0, 0, -1), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 7, 23, 68, 238, 808, 2938, 10616, 40070, 151690, 586723, 2285518, 9042529, 36023276, 144911726, 586960584, 2396089239, 9837755873, 40629129008, 168667408199, 703695471412, 2948667510395, 12406647625358, 52403123154991, 222135049283566, 944740421631064, 4030480584427033

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, 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: A148693 A148694 A148695 * A148697 A148698 A148699

Adjacent sequences: A148693 A148694 A148695 * A148697 A148698 A148699

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved