A149405 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, 1), (1, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 52, 185, 835, 3281, 15158, 63309, 296887, 1289845, 6111674, 27277697, 130232632, 592619901, 2845730366, 13138353029, 63376378401, 295889267987, 1432525057484, 6747494887431, 32765754206296, 155437488129585, 756701050408249, 3610745322320158, 17615328569640258, 84463982275069381

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A149403 A127866 A149404 * A149406 A149407 A149408

Adjacent sequences: A149402 A149403 A149404 * A149406 A149407 A149408

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved