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A156573 a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=529, a(2)=13225. 3

%I

%S 529,13225,444889,15108769,513249025,17435353849,592288777609,

%T 20120383080625,683500735959409,23218904639535049,788759257008228025,

%U 26794595833640213569,910227499086759029089,30920940373116166771225

%N a(n) = 34*a(n-1)-a(n-2)-4232 for n > 2; a(1)=529, a(2)=13225.

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

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

%F a(n) = 529*(2+(3-2*sqrt(2))*(17+12*sqrt(2))^n+(3+2*sqrt(2))*(17-12*sqrt(2))^n)/8.

%F G.f.: 529*x*(1-10*x+x^2)/((1-x)*(1-34*x+x^2)).

%e a(3) = 34*a(2)-a(1)-4232 = 34*13225-529-4232 = 444889.

%o (PARI) {m=14; v=concat([529, 13225], vector(m-2)); for(n=3, m, v[n]=34*v[n-1]-v[n-2]-4232); v}

%Y Second trisection of A156572. Equals 529*A008844.

%Y Cf. A156164 (decimal expansion of 17+12*sqrt(2)), A156574, A156575.

%K nonn,easy

%O 1,1

%A _Klaus Brockhaus_, Feb 11 2009

%E Revised by _Klaus Brockhaus_, Feb 16 2009

%E G.f. corrected by _Klaus Brockhaus_, Sep 22 2009

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Last modified September 24 06:13 EDT 2021. Contains 347623 sequences. (Running on oeis4.)