A149324 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, 0, 0), (-1, 0, 1), (0, -1, 0), (0, 0, -1), (1, 1, 0)}.

1, 1, 4, 12, 38, 140, 524, 1945, 7607, 30451, 121729, 495258, 2052186, 8535846, 35743505, 151371003, 644849874, 2757517776, 11867704367, 51360479505, 223020860987, 972134840405, 4255707686907, 18690007639491, 82306784548572, 363581658945791, 1610644675412670, 7151507718739511

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, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A014345 A006192 A354341 * A149325 A149326 A149327

Adjacent sequences: A149321 A149322 A149323 * A149325 A149326 A149327

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved