A150524 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, 1, -1), (1, -1, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 25, 104, 427, 1899, 8291, 38116, 172204, 807165, 3725853, 17684156, 82829235, 396549703, 1876918889, 9042415994, 43135495220, 208799652974, 1002092645192, 4868589896196, 23478133382026, 114402790368063, 553837110378969, 2705185725395615, 13138030962744806, 64299909697749916

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150521 A150522 A150523 * A150525 A150526 A150527

Adjacent sequences: A150521 A150522 A150523 * A150525 A150526 A150527

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved