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Search: id:A130861
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| A130861 |
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Ratio of Sum of k^2-1 to sum of k made into an integer sequence: (n-1)*(2*n+5). |
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+0
7
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| 0, 9, 22, 39, 60, 85, 114, 147, 184, 225, 270, 319, 372, 429, 490, 555, 624, 697, 774, 855, 940, 1029, 1122, 1219, 1320, 1425, 1534, 1647, 1764, 1885, 2010, 2139, 2272, 2409, 2550, 2695, 2844, 2997, 3154, 3315, 3480, 3649, 3822, 3999, 4180, 4365
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n) = 3*(n + 1)*Sum[k^2 - 1, {k, 1, n}]/Sum[k, {k, 1, n}]=(-1 + n) (5 + 2 n)
G.f.: x^2*(-9+5*x)/(-1+x)^3. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
a(n)=4*n+a(n-1)+1 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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EXAMPLE
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For n=2, a(2)=4*2+0+1=9; n=3, a(3)=4*3+9+1=22; n=4, a(4)=4*4+22+1=39 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009]
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MAPLE
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with(finance):seq(add(cashflows([n, k, k], 0), k=3..n), n=2..30); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 22 2008]
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MATHEMATICA
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f0[n_] = 3*(n + 1)*Sum[k^2 - 1, {k, 1, n}]/Sum[k, {k, 1, n}]; Table[f0[n], {n, 1, 30}]
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CROSSREFS
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Sequence in context: A146681 A050860 A154528 this_sequence A049730 A131895 A113519
Adjacent sequences: A130858 A130859 A130860 this_sequence A130862 A130863 A130864
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KEYWORD
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nonn,new
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AUTHOR
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Roger L Bagula (rlbagulatftn(AT)yahoo.com), Jul 22 2007
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EXTENSIONS
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More terms a(31)-a(46) Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 08 2009
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