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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
First differences of A088809.
EXAMPLE
The subset S = {1,3,6,8} has pair-sums {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 pair-sum 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
Partial sums are A088809, non-binary A364534.
With re-usable parts we have differences of A093971, complement A288728.
The complement with n is counted by A364755, partial sums A085489(n) - 1.
Sequence in context: A173769 A067038 A209398 * A175660 A365069 A347079
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 11 2023
EXTENSIONS
a(16) onwards added (using A088809) by Andrew Howroyd, Jan 13 2024
STATUS
approved

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Last modified March 4 13:15 EST 2024. Contains 370532 sequences. (Running on oeis4.)