A149772 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, 1), (-1, 1, 1), (0, -1, 1), (0, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 77, 319, 1375, 5929, 26113, 115305, 514955, 2306707, 10404785, 47061877, 213869821, 974273885, 4453345549, 20398856593, 93680104321, 431003385037, 1987028917979, 9175200503077, 42438133734509, 196561080317075, 911699027477733, 4233825192549621, 19685174568501545, 91624550919104045

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[i, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A108981 A228678 A149771 * A370194 A149773 A363548

Adjacent sequences: A149769 A149770 A149771 * A149773 A149774 A149775

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved