A149109 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, 1, 0), (1, -1, -1), (1, 1, 0)}.

1, 1, 4, 8, 35, 98, 437, 1390, 6414, 22044, 103172, 374503, 1774645, 6683511, 31944939, 123925869, 595885731, 2363708500, 11425995739, 46163399205, 223969482276, 918579161523, 4471597359752, 18570784802630, 90632373360272, 380475962435925, 1861020909988149, 7884480596635018, 38637512673187517

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[-1 + 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, -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: A324410 A218628 A149108 * A266676 A046056 A158863

Adjacent sequences: A149106 A149107 A149108 * A149110 A149111 A149112

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved