A154379 - OEIS

%I #30 May 12 2019 19:28:07

%S 260,510,760,1010,1260,1510,1760,2010,2260,2510,2760,3010,3260,3510,

%T 3760,4010,4260,4510,4760,5010,5260,5510,5760,6010,6260,6510,6760,

%U 7010,7260,7510,7760,8010,8260,8510,8760,9010,9260,9510,9760,10010,10260

%N a(n) = 250*n + 10.

%C The identity (1250*n^2 + 100*n + 1)^2 - (25*n^2 + 2*n)*(250*n + 10)^2 = 1 can be written as A154375(n)^2 - A154377(n)*a(n)^2 = 1 (see also the second comment in A154375). - _Vincenzo Librandi_, Jan 30 2012

%H Vincenzo Librandi, <a href="/A154379/b154379.txt">Table of n, a(n) for n = 1..10000</a>

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

%F a(n) = 2*a(n-1) - a(n-2). - _Vincenzo Librandi_, Jan 30 2012

%F G.f.: 10*x*(26 - x)/(1-x)^2. - _Vincenzo Librandi_, Jan 30 2012 [corrected by _Georg Fischer_, May 12 2019]

%F E.g.f.: 10*( (25*x + 1)*exp(x) - 1). - _G. C. Greubel_, Sep 15 2016

%t LinearRecurrence[{2, -1}, {260, 510}, 50] (* _Vincenzo Librandi_, Jan 30 2012 *)

%o (PARI) a(n)=250*n+10 \\ _Charles R Greathouse IV_, Dec 27 2011

%Y Cf. A154375, A154377.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Jan 08 2009

%E Definition corrected by _Paolo P. Lava_, Jan 14 2009