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A156854
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2025n^2 - 3401n + 1428.
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3
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52, 2726, 9450, 20224, 35048, 53922, 76846, 103820, 134844, 169918, 209042, 252216, 299440, 350714, 406038, 465412, 528836, 596310, 667834, 743408, 823032, 906706, 994430, 1086204, 1182028, 1281902, 1385826, 1493800, 1605824, 1721898
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The identity(32805000*n^2-10513800*n+842401)^2-(2025*n^2-3401*n+1428)*(729000*n-116820)^2=1 can be written as A157079(n)^2-a(n)*A156866(n)^2=1.
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Index to sequences with linear recurrences with constant coefficients, signature (3,-3,1).
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FORMULA
| a(n) = 3*a(n-1) -3*a(n-2) +a(n-3).
G.f.: x*(-52-2570*x-1428*x^2)/(x-1)^3.
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MATHEMATICA
| LinearRecurrence[{3, -3, 1}, {52, 2726, 9450}, 40]
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PROG
| (MAGMA) I:=[52, 2726, 9450]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]];
(PARI) a(n)=2025*n^2-3401*n+1428 \\ Charles R Greathouse IV, Dec 23 2011
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CROSSREFS
| Cf. A156853, A156866, A157079.
Sequence in context: A189776 A189158 A042301 * A027550 A006179 A029809
Adjacent sequences: A156851 A156852 A156853 * A156855 A156856 A156857
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KEYWORD
| nonn,easy
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AUTHOR
| Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 17 2009
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