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A056914 a(n) = L(4*n+1) where L() are the Lucas numbers. 7

%I

%S 1,11,76,521,3571,24476,167761,1149851,7881196,54018521,370248451,

%T 2537720636,17393796001,119218851371,817138163596,5600748293801,

%U 38388099893011,263115950957276,1803423556807921,12360848946698171

%N a(n) = L(4*n+1) where L() are the Lucas numbers.

%D V. E. Hoggatt, Jr., Fibonacci and Lucas Numbers, A Publication of the Fibonacci Association, Houghton Mifflin Co., 1969, pp. 27-29.

%H G. C. Greubel, <a href="/A056914/b056914.txt">Table of n, a(n) for n = 0..1000</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (7,-1).

%F a(n) = 7*a(n-1) - a(n-2); a(0)=1, a(1)=11.

%F G.f.: (1+4*x)/(1-7*x+x^2). - _Philippe Deléham_, Nov 02 2008

%e a(n)={11*[((7+3*sqrt(5))/2)^n - ((7-3*sqrt(5))/2)^n]-[((7+3*sqrt(5))/2)^(n-1) - ((7-3*sqrt(5))/2)^(n-1)]}/3*sqrt(5).

%t CoefficientList[Series[(1 + 4*x)/(1 - 7*x + x^2), {x, 0, 50}], x] (* or *) LinearRecurrence[{7,-1}, {1,11}, 30] (* _G. C. Greubel_, Dec 24 2017 *)

%o (PARI) x='x+O('x^30); Vec((1+4*x)/(1-7*x+x^2)) \\ _G. C. Greubel_, Dec 24 2017

%o (MAGMA) I:=[1,11]; [n le 2 select I[n] else 7*Self(n-1) - Self(n-2): n in [1..30]]; // _G. C. Greubel_, Dec 24 2017

%Y Cf. (A056914)=sqrt{5*(A033889)^2-4}.

%Y Cf. quadrisection of A000032: A056854 (first), this sequence (second), A246453 (third, without 11), A288913 (fourth).

%K easy,nonn

%O 0,2

%A _Barry E. Williams_, Jul 11 2000

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Last modified November 14 02:19 EST 2019. Contains 329108 sequences. (Running on oeis4.)