A149713 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, 0, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 71, 289, 1269, 5529, 24779, 111551, 509963, 2340953, 10839905, 50411789, 235844465, 1107194945, 5219661875, 24680610811, 117075851463, 556728580407, 2654084789355, 12679171087595, 60696272736839, 291070028708913, 1398220437952441, 6726843557751409, 32409881516115509, 156354857436362549

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, 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: A149711 A149712 A017957 * A149714 A149715 A149716

Adjacent sequences: A149710 A149711 A149712 * A149714 A149715 A149716

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved