A364756 - OEIS

A364756

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

%I #10 Jan 13 2024 16:46:38

%S 0,0,0,1,2,7,17,40,87,196,413,875,1812,3741,7640,15567,31493,63666,

%T 128284,257977,518045,1039478,2083719,4174586,8359837,16735079,

%U 33493780,67020261,134090173,268250256,536609131,1073358893,2146942626,4294183434,8588837984,17178273355

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

%H Andrew Howroyd, <a href="/A364756/b364756.txt">Table of n, a(n) for n = 0..75</a>

%F First differences of A088809.

%e 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).

%e The subset {2,3,4,6} has pair-sum 2 + 4 = 6, so is counted under a(6).

%e The a(0) = 0 through a(6) = 17 subsets:

%e . . . {1,2,3} {1,3,4} {1,4,5} {1,5,6}

%e {1,2,3,4} {2,3,5} {2,4,6}

%e {1,2,3,5} {1,2,3,6}

%e {1,2,4,5} {1,2,4,6}

%e {1,3,4,5} {1,2,5,6}

%e {2,3,4,5} {1,3,4,6}

%e {1,2,3,4,5} {1,3,5,6}

%e {1,4,5,6}

%e {2,3,4,6}

%e {2,3,5,6}

%e {2,4,5,6}

%e {1,2,3,4,6}

%e {1,2,3,5,6}

%e {1,2,4,5,6}

%e {1,3,4,5,6}

%e {2,3,4,5,6}

%e {1,2,3,4,5,6}

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

%Y Partial sums are A088809, non-binary A364534.

%Y With re-usable parts we have differences of A093971, complement A288728.

%Y The complement with n is counted by A364755, partial sums A085489(n) - 1.

%Y Cf. A000079, A007865, A050291, A051026, A103580, A151897, A236912, A326080, A326083, A364272.

%K nonn

%O 0,5

%A _Gus Wiseman_, Aug 11 2023

%E a(16) onwards added (using A088809) by _Andrew Howroyd_, Jan 13 2024