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A033994
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a(n) = n*(n+1)*(5*n+1)/6.
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16
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2, 11, 32, 70, 130, 217, 336, 492, 690, 935, 1232, 1586, 2002, 2485, 3040, 3672, 4386, 5187, 6080, 7070, 8162, 9361, 10672, 12100, 13650, 15327, 17136, 19082, 21170, 23405, 25792, 28336, 31042, 33915, 36960, 40182, 43586, 47177, 50960, 54940
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OFFSET
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1,1
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COMMENTS
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a(n) is the dot product of the vectors of the first n positive integers and the next n integers. - Michel Marcus, Sep 02 2020
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REFERENCES
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A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 194-196.
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LINKS
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FORMULA
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G.f.: x*(2+3*x)/(1-x)^4.
Sum_{n>=1} 1/a(n) = 36 - 3*Pi*5^(3/4)*phi^(3/2)/4 - 15*sqrt(5)*log(phi)/4 - 75*log(5)/8 = 0.66131826232008423794478..., where phi = A001622 = (1 + sqrt(5))/2 is the golden ratio. - Vaclav Kotesovec, Jun 01 2018
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MAPLE
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MATHEMATICA
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Table[Range[x].Range[x+1, 2x], {x, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 11, 32, 70}, 40] (* Harvey P. Dale, Jun 01 2018 *)
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PROG
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(PARI) a(n) = n*(n+1)*(5*n+1)/6;
(GAP) a:=List([1..40], n->n*(n+1)*(5*n+1)/6);; Print(a); # Muniru A Asiru, Jan 01 2019
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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