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Search: id:A087076
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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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+0
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
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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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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FORMULA
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a(n) = (2^(n-2))*n*(n+1)*(2*n+1)/3.
G.f.: x(1+2x)/(1-2x)^4.
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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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CROSSREFS
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Cf. A058645 has the same then similar initial values.
Equals A014483 shifted right.
Sequence in context: A002889 A055911 A014483 this_sequence A116971 A034195 A067250
Adjacent sequences: A087073 A087074 A087075 this_sequence A087077 A087078 A087079
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KEYWORD
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base,easy,nonn
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AUTHOR
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Alan Sutcliffe (alansut(AT)ntlworld.com), Aug 08 2003
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