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A075667
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Sum of next n 6th powers.
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1
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1, 793, 66377, 1911234, 28504515, 271739011, 1874885963, 10136389172, 45311985069, 173957200405, 589679082421, 1802148522758, 5045944649967, 13108508706879, 31915866810295, 73427944186856, 160710828298553, 336507487921137, 677266380588289, 1315464522556810
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OFFSET
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1,2
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..1000
Index to sequences with linear recurrences with constant coefficients, signature (14,-91,364,-1001,2002,-3003,3432,-3003,2002,-1001,364,-91,-14,1]).
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FORMULA
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a(1)=1; a(n)=sum(i^s, {i, n(n-1)/2+1, n(n-1)/2+1+n}).
a(n)=(21n^13 + 231n^11 + 693n^9 + 549n^7 - 126n^5 - 56n^3 + 32n)/1344.
G.f.: x*(x^12 +779*x^11 +55366*x^10 +1053755*x^9 +7499895*x^8 +23228658*x^7 +33620292*x^6 +23228658*x^5 +7499895*x^4 +1053755*x^3 +55366*x^2 +779*x +1)/(x-1)^14. [Colin Barker, Jul 22 2012]
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EXAMPLE
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s=6; a(1) = 1^s = 1; a(2) = 2^s + 3^s = 2^6 + 3^6 = 793; a(3) = 4^s + 5^s + 6^s = 66377, a(4) = 7^s + 8^s + 9^s + 10^3 = 1911234.
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MATHEMATICA
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i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=6; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
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CROSSREFS
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Cf. A072474 (s=2), A075664 - A075670 (s=3-10), A075671 (s=n).
Cf. A006003, A072474, A075664 - A075671.
Sequence in context: A130555 A133537 A213471 * A136543 A133274 A086393
Adjacent sequences: A075664 A075665 A075666 * A075668 A075669 A075670
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KEYWORD
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nonn,easy
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AUTHOR
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Zak Seidov, Sep 24 2002
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EXTENSIONS
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Formula from Charles R Greathouse IV, Sep 17 2009
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STATUS
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approved
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