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A157664
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a(n) = 80000*n^2 + 800*n + 1.
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3
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80801, 321601, 722401, 1283201, 2004001, 2884801, 3925601, 5126401, 6487201, 8008001, 9688801, 11529601, 13530401, 15691201, 18012001, 20492801, 23133601, 25934401, 28895201, 32016001, 35296801, 38737601, 42338401, 46099201
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OFFSET
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1,1
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COMMENTS
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The identity (80000n^2 + 800n + 1)^2 - (100n^2 + n)*(8000n + 40)^2 = 1 can be written as a(n)^2 - A055438(n)*A157663(n)^2 = 1. - Vincenzo Librandi, Feb 04 2012
This is the case s=10 of the identity (8*n^2*s^4 + 8*n*s^2 + 1)^2 - (n^2*s^2 + n)*(8*n*s^3 + 4*s)^2 = 1. - Bruno Berselli, Feb 04 2012
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LINKS
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FORMULA
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E.g.f.: (1 + 80800*x + 80000*x^2)*exp(x) - 1. - G. C. Greubel, Nov 17 2018
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {80801, 321601, 722401}, 50] (* Vincenzo Librandi, Feb 04 2012 *)
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PROG
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(Magma) I:=[80801, 321601, 722401]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 04 2012
(PARI) for(n=1, 40, print1(80000*n^2 + 800*n + 1", ")); \\ Vincenzo Librandi, Feb 04 2012
(Sage) [80000*n^2+800*n+1 for n in (1..40)] # G. C. Greubel, Nov 17 2018
(GAP) List([1..40], n -> 80000*n^2+800*n+1); # G. C. Greubel, Nov 17 2018
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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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