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A154295 a(n) = 81*n^2 - 90*n + 26. 4

%I

%S 26,17,170,485,962,1601,2402,3365,4490,5777,7226,8837,10610,12545,

%T 14642,16901,19322,21905,24650,27557,30626,33857,37250,40805,44522,

%U 48401,52442,56645,61010,65537,70226,75077,80090,85265,90602,96101,101762

%N a(n) = 81*n^2 - 90*n + 26.

%C The identity (81*n^2 + 72*n + 17)^2 - (9*n^2 + 8*n + 2)*(27*n + 12)^2 = 1 can be written as a(n+1)^2 - A154262(n+1)*A154266(n)^2 = 1. - _Vincenzo Librandi_, Feb 03 2012

%H Vincenzo Librandi, <a href="/A154295/b154295.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = A002522(|9n-5|). - _R. J. Mathar_, Jan 07 2009

%F G.f.: (26 - 61*x + 197*x^2)/(1 - x)^3. - _Vincenzo Librandi_, Feb 03 2012

%F a(n) = 3*a(n-1) -3*a(n-2) +a(n-3). - _Vincenzo Librandi_, Feb 03 2012

%F E.g.f.: (26 - 9*x + 81*x^2)*exp(x). - _G. C. Greubel_, Sep 10 2016

%t LinearRecurrence[{3, -3, 1}, {26, 17, 170}, 40] (* _Vincenzo Librandi_, Feb 03 2012 *)

%t Table[81*n^2 - 90*n + 26,{n,0,25}] (* _G. C. Greubel_, Sep 10 2016 *)

%o (MAGMA) I:=[26, 17, 170]; [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 03 2012

%o (PARI) for(n=0, 22, print1(81*n^2-90*n+26", ")); \\ _Vincenzo Librandi_, Feb 03 2012

%o (PARI) x='x+O('x^99); Vec((26-61*x+197*x^2)/(1-x)^3) \\ _Altug Alkan_, Sep 10 2016

%Y Cf. A154262, A154266.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Jan 06 2009

%E Corrected by _Don Reble_, Jun 16 2010

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Last modified October 22 22:34 EDT 2019. Contains 328335 sequences. (Running on oeis4.)