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A154374
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a(n) = 1250*n^2 - 100*n + 1.
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3
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1151, 4801, 10951, 19601, 30751, 44401, 60551, 79201, 100351, 124001, 150151, 178801, 209951, 243601, 279751, 318401, 359551, 403201, 449351, 498001, 549151, 602801, 658951, 717601, 778751, 842401, 908551, 977201, 1048351, 1122001
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OFFSET
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1,1
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COMMENTS
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The identity (1250*n^2 - 100*n + 1)^2 - (25*n^2 - 2*n)*(250*n - 10)^2 = 1 can be written as a(n)^2 - A154376(n)*A154378(n)^2 = 1. - Vincenzo Librandi, Jan 30 2012
This is the case s = 5 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - Bruno Berselli, Jan 30 2012
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LINKS
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FORMULA
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E.g.f.: -1 + (1 + 1150*x + 1250*x^2)*exp(x). - G. C. Greubel, Sep 15 2016
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {1151, 4801, 10951}, 40] (* Vincenzo Librandi, Jan 30 2012 *)
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PROG
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(Magma) I:=[1151, 4801, 10951]; [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, Jan 30 2012
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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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