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A268344 a(n) = 11*a(n - 1) - 3*a(n - 2) for n>1, a(0)=0, a(1)=1. 1

%I

%S 0,1,11,118,1265,13561,145376,1558453,16706855,179100046,1919979941,

%T 20582479213,220647331520,2365373209081,25357163305331,

%U 271832676731398,2914087954129385,31239469465229041,334891900255131296,3590092494410757133

%N a(n) = 11*a(n - 1) - 3*a(n - 2) for n>1, a(0)=0, a(1)=1.

%C In general, the ordinary generating function for the recurrence relation b(n) = k*b(n - 1) - m*b(n - 2), with n>1 and b(0)=0, b(1)=1, is x/(1 - k*x + m*x^2). This recurrence gives the closed form b(n) = (2^(-n)*((sqrt(k^2 - 4*m) + k)^n - (k - sqrt(k^2 - 4*m))^n))/sqrt(k^2 - 4*m).

%H G. C. Greubel, <a href="/A268344/b268344.txt">Table of n, a(n) for n = 0..965</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-3).

%F G.f.: x/(1 - 11*x + 3*x^2).

%F a(n) = ( ((11 + sqrt(109))/2)^n - ((11 - sqrt(109))/2)^n )/sqrt(109).

%t LinearRecurrence[{11, -3}, {0, 1}, 20] (* or *) Table[(((11 + Sqrt[109])/2)^n - ((11 - Sqrt[109])/2)^n)/Sqrt[109], {n, 0, 20}]

%o (PARI) x='x+O('x^30); concat([0], Vec(x/(1-11*x+3*x^2))) \\ _G. C. Greubel_, Jan 14 2018

%o (MAGMA) I:=[0,1]; [n le 2 select I[n] else 11*Self(n-1) - 3*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 14 2018

%Y Cf. A190872, A190980.

%K nonn,easy

%O 0,3

%A _Ilya Gutkovskiy_, Feb 02 2016

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Last modified October 18 22:40 EDT 2018. Contains 316327 sequences. (Running on oeis4.)