A148682 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), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 7, 22, 66, 227, 758, 2723, 9807, 36535, 136783, 525245, 2031029, 7958899, 31458447, 125716531, 505462106, 2048274371, 8355777974, 34294187162, 141446086258, 586560299481, 2443831656620, 10223955384759, 42941361160034, 181064797061248, 766076071152554, 3251480803772371

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, -1 + j, k, -1 + n] + aux[-1 + i, j, 1 + 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: A166135 A007595 A148681 * A148683 A148684 A148685

Adjacent sequences: A148679 A148680 A148681 * A148683 A148684 A148685

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved