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A036659
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Product of n with sum of next n consecutive integers.
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6
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2, 14, 45, 104, 200, 342, 539, 800, 1134, 1550, 2057, 2664, 3380, 4214, 5175, 6272, 7514, 8910, 10469, 12200, 14112, 16214, 18515, 21024, 23750, 26702, 29889, 33320, 37004, 40950, 45167, 49664, 54450, 59534, 64925, 70632, 76664, 83030, 89739, 96800, 104222, 112014
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OFFSET
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1,1
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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a(n) = 2 + (3*n*n + 10*n + 11)*n/2. - Frank Ellermann, Mar 16 2002
a(n) = n^2(3n + 1)/2. - Ronnie B Kon (ronniekon(AT)yahoo.com), Jun 09 2006
G.f.: x*(2 + 6*x + x^2)/(1 - x)^4. - Colin Barker, Mar 27 2012
From Amiram Eldar, Jan 10 2023: (Start)
Sum_{n>=1} 1/a(n) = Pi^2/3 + sqrt(3)*Pi + 9*log(3) - 18.
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/6 - 2*sqrt(3)*Pi - 12*log(2) + 18. (End)
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EXAMPLE
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n=3 -> 3*(4+5+6)=45
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MATHEMATICA
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CoefficientList[Series[(2+6*x+x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 25 2012 *)
Table[(n^2*(1+3n))/2, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 14, 45, 104}, 40] (* Harvey P. Dale, Jan 04 2015 *)
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PROG
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(PARI) a(n)=n^2*(3*n+1)/2 \\ Charles R Greathouse IV, Dec 08 2011
(Magma) I:=[2, 14, 45, 104]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Apr 25 2012
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CROSSREFS
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Cf. A036660.
Sequence in context: A085929 A231247 A318764 * A079937 A324915 A281760
Adjacent sequences: A036656 A036657 A036658 * A036660 A036661 A036662
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KEYWORD
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nonn,easy
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AUTHOR
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G. L. Honaker, Jr., Dec 15 1998
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STATUS
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approved
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