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A075670
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Sum of next n 9-th powers.
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9
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1, 20195, 12292965, 1561991824, 77226633575, 2014634387961, 33098483802475, 383318212734080, 3377498614484589, 23898971839102975, 141290020118952881, 719054471032657200, 3223613105991831475, 12964037775857022869
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
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FORMULA
| a(1)=1; a(n)=sum(i^s, {i, n(n-1)/2+1, n(n-1)/2+1+n}).
a(n) = (5n^19 + 105n^17 + 666n^15 + 1530n^13 + 689n^11 - 995n^9 + 304n^7 + 640n^5 - 384n^3)/2560
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EXAMPLE
| s=9; a(1) = 1^s = 1; a(2) = 2^s + 3^s = 2^9 + 3^9 = 20195; a(3) = 4^s + 5^s + 6^s = 12292965, a(4) = 7^s + 8^s + 9^s + 10^3 = 1561991824.
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MATHEMATICA
| i1 := n(n-1)/2+1; i2 := n(n-1)/2+n; s=9; Table[Sum[i^s, {i, i1, i2}], {n, 20}]
Total[#^9]&/@(Range[First[#]+1, Last[#]]&/@Partition[Accumulate[Range[ 0, 15]], 2, 1]) (* From Harvey P. Dale, Oct 05 2011 *)
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PROG
| (MAGMA) [(5*n^19 + 105*n^17 + 666*n^15 + 1530*n^13 + 689*n^11 - 995*n^9 + 304*n^7 + 640*n^5 - 384*n^3)/2560 : n in [1..20]]; // Vincenzo Librandi, Oct 06 2011
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CROSSREFS
| Cf. A072474 (s=2), A075664 - A075670 (s=3-10), A075671 (s=n).
Cf. A006003, A072474, A075664 - A075671.
Sequence in context: A114613 A052358 A052189 * A053073 A133527 A146961
Adjacent sequences: A075667 A075668 A075669 * A075671 A075672 A075673
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KEYWORD
| nonn,easy
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AUTHOR
| Zak Seidov (zakseidov(AT)yahoo.com), Sep 24 2002
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EXTENSIONS
| Formula from Charles R Greathouse IV (charles.greathouse(AT)case.edu), Sep 17 2009
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