A148093 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, -1, 1), (0, 1, 0), (1, 0, -1)}.

1, 1, 2, 4, 10, 25, 70, 212, 639, 2000, 6451, 21617, 71791, 246306, 858806, 3031680, 10707284, 38611784, 140802398, 514700655, 1893610027, 7056144208, 26475930759, 99365898413, 375942742181, 1434074803915, 5489981644607, 21037233338679, 81212735932262, 315232763329880, 1225469410310123, 4774478236859757

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[i, 1 + 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: A005817 A302093 A292617 * A206289 A148094 A148095

Adjacent sequences: A148090 A148091 A148092 * A148094 A148095 A148096

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved