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A262142
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The first of ten consecutive positive integers the sum of the squares of which is equal to the sum of the squares of nine consecutive positive integers.
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2
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171, 6660, 253071, 9610200, 364934691, 13857908220, 526235577831, 19983094049520, 758831338304091, 28815607761506100, 1094234263598927871, 41552086408997753160, 1577885049278315692371, 59918079786166998557100, 2275309146825067629477591
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OFFSET
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1,1
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COMMENTS
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For the first of the corresponding nine consecutive positive integers, see A262141.
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LINKS
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FORMULA
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a(n) = 39*a(n-1)-39*a(n-2)+a(n-3) for n>3.
G.f.: 9*x*(x-19) / ((x-1)*(x^2-38*x+1)).
a(n) = 3*(-6-(-3+sqrt(10))*(19+6*sqrt(10))^(-n)+(3+sqrt(10))*(19+6*sqrt(10))^n)/4. - Colin Barker, Mar 03 2016
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EXAMPLE
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171 is in the sequence because 171^2 + ... + 180^2 = 308085 = 181^2 + ... + 189^2.
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MATHEMATICA
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LinearRecurrence[{39, -39, 1}, {171, 6660, 253071}, 30] (* Harvey P. Dale, Sep 26 2015 *)
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PROG
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(PARI) Vec(9*x*(x-19)/((x-1)*(x^2-38*x+1)) + O(x^30))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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