A149669 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), (0, -1, 1), (0, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 63, 253, 1033, 4255, 17935, 76417, 328111, 1422019, 6205767, 27220843, 120065915, 531976191, 2365738953, 10559780719, 47286444233, 212333994419, 956041766143, 4315020289809, 19517499482841, 88463974798857, 401726989350349, 1827449753524945, 8326788750143589, 37999196458199753

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + 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: A099528 A149667 A149668 * A149670 A149671 A366978

Adjacent sequences: A149666 A149667 A149668 * A149670 A149671 A149672

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved