A151081 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), (0, 1, 0), (1, 0, 1), (1, 1, 0)}.

1, 3, 10, 41, 170, 734, 3271, 14737, 67579, 312183, 1456139, 6839691, 32263003, 153094265, 729036920, 3483249581, 16697234320, 80240947268, 386535282704, 1865769002653, 9023342738455, 43712789051689, 212071691893026, 1030351010376779, 5012234029998176, 24410178281619735, 119009018006099202

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[i, -1 + j, 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: A151079 A151080 A153474 * A152802 A260789 A151082

Adjacent sequences: A151078 A151079 A151080 * A151082 A151083 A151084

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved