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Search: id:A007654
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| A007654 |
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Numbers n such that standard deviation of 1,...,n is an integer.
(Formerly M3154)
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+0
11
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| 0, 3, 48, 675, 9408, 131043, 1825200, 25421763, 354079488, 4931691075, 68689595568, 956722646883, 13325427460800, 185599261804323, 2585064237799728, 36005300067391875, 501489136705686528
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Gives solutions to the Diophantine equation k=sqrt[n*(n+1)/3]. - Anton Lorenz Vrba (anton(AT)a-l-v.net), Jun 28 2005
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REFERENCES
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D. A. Benaron, personal communication.
E. Keith Lloyd, The standard deviation of 1,2, ..., n - Pell's equation and rational triangles, Math. Gaz. vol 81 no 491 (1997) pp 231-243.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..100
Tanya Khovanova, Recursive Sequences
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FORMULA
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3*(A001353)^2.
a(m) = 14a(m-1) - a(m-2) + 6.
G.f.: -3*x^2*(1+x)/(-1+x)/(1-14*x+x^2) = -3+1/2/(-1+x)+1/2*(-97*x+7)/(1-14*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 20 2007
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CROSSREFS
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Cf. A007655.
Adjacent sequences: A007651 A007652 A007653 this_sequence A007655 A007656 A007657
Sequence in context: A073982 A081540 A024042 this_sequence A001080 A099852 A003029
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KEYWORD
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easy,nonn
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AUTHOR
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njas
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EXTENSIONS
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Corrected by Keith Lloyd Mar 15, 1996.
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