

A364756


Number of subsets of {1..n} containing n and some element equal to the sum of two distinct others.


14



0, 0, 0, 1, 2, 7, 17, 40, 87, 196, 413, 875, 1812, 3741, 7640, 15567, 31493, 63666, 128284, 257977, 518045, 1039478, 2083719, 4174586, 8359837, 16735079, 33493780, 67020261, 134090173, 268250256, 536609131, 1073358893, 2146942626, 4294183434, 8588837984, 17178273355
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,5


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 not counted under a(8).
The subset {2,3,4,6} has pairsum 2 + 4 = 6, so is counted under a(6).
The a(0) = 0 through a(6) = 17 subsets:
. . . {1,2,3} {1,3,4} {1,4,5} {1,5,6}
{1,2,3,4} {2,3,5} {2,4,6}
{1,2,3,5} {1,2,3,6}
{1,2,4,5} {1,2,4,6}
{1,3,4,5} {1,2,5,6}
{2,3,4,5} {1,3,4,6}
{1,2,3,4,5} {1,3,5,6}
{1,4,5,6}
{2,3,4,6}
{2,3,5,6}
{2,4,5,6}
{1,2,3,4,6}
{1,2,3,5,6}
{1,2,4,5,6}
{1,3,4,5,6}
{2,3,4,5,6}
{1,2,3,4,5,6}


MATHEMATICA

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


CROSSREFS

With reusable parts we have differences of A093971, complement A288728.
The complement with n is counted by A364755, partial sums A085489(n)  1.


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



