

A364755


Number of subsets of {1..n} containing n but not containing the sum of any two distinct elements.


15



0, 1, 2, 3, 6, 9, 15, 24, 41, 60, 99, 149, 236, 355, 552, 817, 1275, 1870, 2788, 4167, 6243, 9098, 13433, 19718, 28771, 42137, 60652, 88603, 127555, 185200, 261781, 382931, 541022, 783862, 1096608, 1595829, 2217467, 3223064, 4441073, 6465800, 8893694
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,3


LINKS



FORMULA



EXAMPLE

The subset S = {1,3,6,8} has pairsums {4,7,9,11,14}, which are disjoint from S, so it is counted under a(8).
The a(1) = 1 through a(6) = 15 subsets:
{1} {2} {3} {4} {5} {6}
{1,2} {1,3} {1,4} {1,5} {1,6}
{2,3} {2,4} {2,5} {2,6}
{3,4} {3,5} {3,6}
{1,2,4} {4,5} {4,6}
{2,3,4} {1,2,5} {5,6}
{1,3,5} {1,2,6}
{2,4,5} {1,3,6}
{3,4,5} {1,4,6}
{2,3,6}
{2,5,6}
{3,4,6}
{3,5,6}
{4,5,6}
{3,4,5,6}


MATHEMATICA

Table[Length[Select[Subsets[Range[n]], MemberQ[#, n]&&Intersection[#, Total/@Subsets[#, {2}]]=={}&]], {n, 0, 10}]


CROSSREFS

With reusable parts we have A288728.
The complement with n is counted by A364756, first differences of A088809.
Cf. A007865, A050291, A054519, A093971, A151897, A236912, A326020, A326080, A326083, A364272, A364349, A364533.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



