A154361 - OEIS

%I #31 Sep 08 2022 08:45:40

%S -70,180,430,680,930,1180,1430,1680,1930,2180,2430,2680,2930,3180,

%T 3430,3680,3930,4180,4430,4680,4930,5180,5430,5680,5930,6180,6430,

%U 6680,6930,7180,7430,7680,7930,8180,8430,8680,8930,9180

%N a(n) = 250*n - 70.

%C The identity (1250*n^2 - 700*n + 99)^2 - (25*n^2 - 14*n + 2)*(250*n - 70)^2 = 1 can be written as A154359(n)^2 - A154357(n)*a(n)^2 = 1. See also the third comment in A154357.

%H Vincenzo Librandi, <a href="/A154361/b154361.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F G.f.: -10*(7 - 32*x)/(1-x)^2. - _Bruno Berselli_, Dec 13 2011

%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Feb 21 2012

%F E.g.f.: 10*(-7 + 25*x)*exp(x). - _G. C. Greubel_, Sep 15 2016

%t LinearRecurrence[{2, -1}, {-70, 180}, 50] (* _Vincenzo Librandi_, Feb 21 2012 *)

%t 250*Range[0,50]-70 (* _Harvey P. Dale_, Apr 09 2020 *)

%o (PARI) for(n=0, 50, print1(250*n - 70", ")); \\ _Vincenzo Librandi_, Feb 21 2012

%o (Magma) [250*n-70: n in [0..50]]; // _Bruno Berselli_, Sep 15 2016

%Y Cf. A154360, A154359, A154358, A154357, A154355.

%K sign,easy

%O 0,1

%A _Vincenzo Librandi_, Jan 08 2009

%E Offset changed and Librandi's comment rewritten by _Bruno Berselli_, Dec 13 2011