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 A158553 a(n) = 196*n^2 - 14. 2

%I

%S 182,770,1750,3122,4886,7042,9590,12530,15862,19586,23702,28210,33110,

%T 38402,44086,50162,56630,63490,70742,78386,86422,94850,103670,112882,

%U 122486,132482,142870,153650,164822,176386,188342,200690,213430,226562

%N a(n) = 196*n^2 - 14.

%C The identity (28*n^2 - 1)^2 - (196*n^2 - 14)*(2*n)^2 = 1 can be written as A158554(n)^2 - a(n)*A005843(n)^2 = 1.

%H Vincenzo Librandi, <a href="/A158553/b158553.txt">Table of n, a(n) for n = 1..10000</a>

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

%F G.f.: 14*x*(13 + 16*x - x^2)/(1-x)^3.

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%t LinearRecurrence[{3, -3, 1}, {182, 770, 1750}, 40] (* _Vincenzo Librandi_, Feb 14 2012 *)

%o (MAGMA) I:=[182, 770, 1750]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // _Vincenzo Librandi_, Feb 14 2012

%o (PARI) for(n=1, 40, print1(196*n^2 - 14", ")); \\ _Vincenzo Librandi_, Feb 14 2012

%Y Cf. A005843, A158554.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 21 2009

%E Comment rewritten by _R. J. Mathar_, Oct 16 2009

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Last modified January 25 10:19 EST 2022. Contains 350565 sequences. (Running on oeis4.)