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A157918
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a(n) = 625*n^2 - 25.
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2
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600, 2475, 5600, 9975, 15600, 22475, 30600, 39975, 50600, 62475, 75600, 89975, 105600, 122475, 140600, 159975, 180600, 202475, 225600, 249975, 275600, 302475, 330600, 359975, 390600, 422475, 455600, 489975, 525600, 562475, 600600, 639975
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OFFSET
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1,1
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COMMENTS
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The identity (50*n^2 - 1)^2 - (625*n^2 - 25)*(2*n)^2 = 1 can be written as A157919(n)^2 - a(n)*A005843(n)^2 = 1. - Vincenzo Librandi, Feb 10 2012
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
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G.f.: -25*x*(24 + 27*x - x^2)/(x-1)^3. - Vincenzo Librandi, Feb 10 2012
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 10 2012
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MATHEMATICA
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LinearRecurrence[{3, -3, 1}, {600, 2475, 5600}, 50] (* Vincenzo Librandi, Feb 10 2012 *)
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PROG
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(MAGMA) I:=[600, 2475, 5600]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 10 2012
(PARI) for(n=1, 40, print1(625*n^2 - 25", ")); \\ Vincenzo Librandi, Feb 10 2012
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CROSSREFS
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Cf. A005843, A157919.
Sequence in context: A172244 A090222 A216058 * A092183 A048530 A223463
Adjacent sequences: A157915 A157916 A157917 * A157919 A157920 A157921
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KEYWORD
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nonn,easy
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AUTHOR
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Vincenzo Librandi, Mar 09 2009
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STATUS
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approved
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