A149677 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, 1, 0), (0, 0, -1), (1, -1, 0), (1, 1, 1)}.

1, 1, 5, 17, 65, 273, 1141, 4913, 21757, 95985, 434329, 1968573, 8998853, 41513797, 191940185, 893808309, 4177271209, 19586280777, 92245079185, 435366093701, 2061445246489, 9785084691865, 46540629413881, 221897111004121, 1059736114267041, 5070514539225085, 24301575479538273, 116635223286925777

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[-1 + i, 1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A149674 A149675 A149676 * A273856 A012765 A062613

Adjacent sequences: A149674 A149675 A149676 * A149678 A149679 A149680

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved