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A180921
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a(n) is the square root of the sum of the cubes of the b(n) consecutive integers starting from b(n), where b(n) = A180920.
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2
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1, 2079, 7876385, 30254180671, 116236127290689, 446579144331338591, 1715756954644453458529, 6591937773063166150358655, 25326223208345427203876398721, 97303342974524967600723097592479, 373839418381901692962342398114034081
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OFFSET
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1,2
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COMMENTS
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Colin Barker's linear recurrence conjecture confirmed, see A180920. - Ray Chandler, Jan 12 2024
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LINKS
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FORMULA
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a(n) = b(n)*(31*(a(n-1)/b(n-1)) + 8*sqrt(15*((a(n-1)/b(n-1))^2) + 1)) where b(n) = A180920(n).
a(n) = 3904*a(n-1) - 238206*a(n-2) + 3904*a(n-3) - a(4).
G.f.: x*(x+1)*(x^2-1826*x+1) / ((x^2-3842*x+1)*(x^2-62*x+1)). (End)
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EXAMPLE
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a(3) = 2017*(31*(2079/33) + 8*sqrt(15*((2079/33)^2) + 1)).
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PROG
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(PARI)
default(realprecision, 1000);
b=vector(20, n, if(n==1, t=1, t=round(31*t-14+8*((3*t-1)*(5*t-3))^(1/2))));
vector(#b, n, if(n==1, t=1, t=round(b[n]*(31*(t/b[n-1])+8*(15*((t/b[n-1])^2)+1)^(1/2))))) \\ Colin Barker, Feb 19 2015
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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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