A156161 - OEIS

%I #11 Jun 20 2020 10:15:00

%S 289,7225,243049,8254129,280395025,9525174409,323575532569,

%T 10992042930625,373405884106369,12684808016683609,430910066683134025,

%U 14638257459209870929,497269843546452475249,16892536423120174285225

%N a(n) = 34*a(n-1)-a(n-2)-2312 for n > 2; a(1)=289, a(2)=7225.

%C lim_{n -> infinity} a(n)/a(n-1) = (17+12*sqrt(2)).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (35,-35,1).

%F a(n) = (578+(867-578*sqrt(2))*(17+12*sqrt(2))^n+(867+578*sqrt(2))*(17-12*sqrt(2))^n)/8.

%F G.f.: x*(289-2890*x+289*x^2)/((1-x)*(1-34*x+x^2)). [corrected by _Klaus Brockhaus_, Sep 23 2009]

%F a(1)=289, a(2)=7225, a(3)=243049, a(n) = 35*a(n-1)-35*a(n-2)+a(n-3). - _Harvey P. Dale_, Dec 11 2013

%e a(3) = 34*a(2)-a(1)-2312 = 34*7225-289-2312 = 243049.

%t RecurrenceTable[{a[1]==289,a[2]==7225,a[n]==34a[n-1]-a[n-2]-2312},a,{n,20}] (* or *) LinearRecurrence[{35,-35,1},{289,7225,243049},20] (* _Harvey P. Dale_, Dec 11 2013 *)

%o (PARI) {m=14; v=concat([289, 7225], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-2312); v}

%Y Second trisection of A156159.

%Y Equals 289*A008844. - _Klaus Brockhaus_, Sep 23 2009

%Y Cf. A156164 (decimal expansion of (17+12*sqrt(2))).

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Feb 09 2009