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A365544
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Number of subsets of {1..n} containing two distinct elements summing to n.
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13
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0, 0, 0, 2, 4, 14, 28, 74, 148, 350, 700, 1562, 3124, 6734, 13468, 28394, 56788, 117950, 235900, 484922, 969844, 1979054, 3958108, 8034314, 16068628, 32491550, 64983100, 131029082, 262058164, 527304974, 1054609948, 2118785834, 4237571668, 8503841150, 17007682300
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: 2*x^3/((2*x-1)*(3*x^2-1)).
a(n) = 2 * A167762(n-1) for n>=1. (End)
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EXAMPLE
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The a(1) = 0 through a(5) = 14 subsets:
. . {1,2} {1,3} {1,4}
{1,2,3} {1,2,3} {2,3}
{1,3,4} {1,2,3}
{1,2,3,4} {1,2,4}
{1,3,4}
{1,4,5}
{2,3,4}
{2,3,5}
{1,2,3,4}
{1,2,3,5}
{1,2,4,5}
{1,3,4,5}
{2,3,4,5}
{1,2,3,4,5}
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MATHEMATICA
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Table[Length[Select[Subsets[Range[n]], MemberQ[Total/@Subsets[#, {2}], n]&]], {n, 0, 10}]
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PROG
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(Python)
def A365544(n): return (1<<n) - (3**(n>>1)<<1 if n&1 else 3**(n-1>>1)<<2) if n else 0 # Chai Wah Wu, Aug 30 2024
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CROSSREFS
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For strict partitions we have A140106 shifted left.
The version for partitions is A004526.
The complement is counted by A068911.
For all subsets of elements we have A365376.
A000009 counts subsets summing to n.
A365381 counts subsets with a subset summing to k.
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KEYWORD
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nonn,easy,changed
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AUTHOR
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STATUS
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approved
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