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A156158 a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 25, a(2) = 137. 4

%I

%S 25,137,797,4645,27073,157793,919685,5360317,31242217,182092985,

%T 1061315693,6185801173,36053491345,210135146897,1224757390037,

%U 7138409193325,41605697769913,242495777426153,1413368966787005

%N a(n) = 6*a(n-1)-a(n-2) for n > 2; a(1) = 25, a(2) = 137.

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

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

%F a(n) = ((26+7*sqrt(2))*(3-2*sqrt(2))^n+(26-7*sqrt(2))*(3+2*sqrt(2))^n)/4.

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

%t LinearRecurrence[{6,-1},{25,137},30] (* _Harvey P. Dale_, Jan 02 2019 *)

%o (PARI) {m=19; v=concat([25,137], vector(m-2)); for(n=3, m, v[n]=6*v[n-1]-v[n-2]); v}

%Y Third trisection of A155923.

%Y Cf. A156035 (decimal expansion of 3+2*sqrt(2)), A156156, A156157.

%K nonn,easy

%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

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Last modified July 12 22:46 EDT 2020. Contains 335669 sequences. (Running on oeis4.)