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A087076
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Sums of the squares of the elements in the subsets of the integers 1 to n.
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3
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0, 1, 10, 56, 240, 880, 2912, 8960, 26112, 72960, 197120, 518144, 1331200, 3354624, 8314880, 20316160, 49020928, 116981760, 276430848, 647495680, 1504706560, 3471835136, 7958691840, 18136170496, 41104179200, 92694118400, 208071032832
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OFFSET
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0,3
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COMMENTS
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A000076 gives the number of subsets of 1 to n. A001787 gives the number of elements in the subsets. A001788 gives the sum of the elements.
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LINKS
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FORMULA
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a(n) = 2^(n - 2)*n*(n + 1)*(2*n + 1)/3.
G.f.: x*(1 + 2*x)/(1 - 2*x)^4.
a(n) = 8*a(n-1) - 24*a(n-2) + 32*a(n-3) - 16*a(n-4). - Matthew House, Feb 13 2017
a(n) = (1/2) * Sum_{k=0..n} Sum_{i=0..n} i^2 * C(n,k). - Wesley Ivan Hurt, Sep 21 2017
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EXAMPLE
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a(3)=56 since the subsets of (1,2,3) are ( ) (1) (1,2) (1,3) (1,2,3) (2) (2,3) (3) and the sum of the squares of the elements in these subsets is 56.
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PROG
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(PARI) a(n) = (2^(n-2))*n*(n+1)*(2*n+1)/3 \\ Michel Marcus, Jul 12 2013
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CROSSREFS
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Cf. A058645 has the same then similar initial values.
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KEYWORD
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nonn,easy
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AUTHOR
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Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 08 2003
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STATUS
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approved
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