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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
First differences of A085489.
EXAMPLE
The subset S = {1,3,6,8} has pair-sums {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
Partial sums are A085489(n) - 1, complement counted by A364534.
With re-usable parts we have A288728.
The complement with n is counted by A364756, first differences of A088809.
Sequence in context: A365071 A192671 A080239 * A114323 A355324 A293631
KEYWORD
nonn
AUTHOR
Gus Wiseman, Aug 11 2023
EXTENSIONS
a(21) onwards added (using A085489) by Andrew Howroyd, Jan 13 2024
STATUS
approved

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Last modified February 24 04:32 EST 2024. Contains 370288 sequences. (Running on oeis4.)