A150977 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, 0), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 36, 169, 749, 3620, 16829, 82399, 391822, 1932376, 9315468, 46137134, 224369868, 1114224182, 5451178811, 27118628625, 133243991331, 663673232831, 3271244384521, 16307808997278, 80575657441894, 401939334649959, 1989692637495554, 9929943962723711, 49228973551576867, 245774352819824880

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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A288780 A150975 A150976 * A150978 A121345 A150979

Adjacent sequences: A150974 A150975 A150976 * A150978 A150979 A150980

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved