A156156 - OEIS

%I #5 Jun 30 2023 00:19:01

%S 13,53,305,1777,10357,60365,351833,2050633,11951965,69661157,

%T 406014977,2366428705,13792557253,80388914813,468540931625,

%U 2730856674937,15916599117997,92768738033045,540695829080273,3151406236448593

%N a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 13, a(2) = 53.

%C lim_{n -> infinity} a(n)/a(n-1) = 3+2*sqrt(2).

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6, -1).

%F a(n) = ((50+31*sqrt(2))*(3-2*sqrt(2))^n+(50-31*sqrt(2))*(3+2*sqrt(2))^n)/4.

%F G.f.: x*(13-25*x)/(1-6*x+x^2).

%o (PARI) {m=20; v=concat([13, 53], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

%Y First trisection of A155923.

%Y Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156157, A156158.

%K nonn

%O 1,1

%A _Klaus Brockhaus_, Feb 09 2009

%E Replaced abbreviation by sqrt(2) _Klaus Brockhaus_, Feb 12 2009

%E G.f. corrected by _Klaus Brockhaus_, Sep 23 2009