A148588 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, 0), (-1, 0, 1), (-1, 1, 0), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 6, 20, 55, 184, 591, 2022, 7046, 24888, 90207, 328888, 1221276, 4569389, 17273315, 65853981, 252762675, 977445345, 3800281869, 14860432632, 58393802535, 230495750196, 913747733984, 3635844012953, 14520010283040, 58176362311273, 233814078106841, 942421272344815, 3808670709979013

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A148586 A148587 A186409 * A148589 A148590 A363592

Adjacent sequences: A148585 A148586 A148587 * A148589 A148590 A148591

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved