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Expansion of (1-4x)/(1-8x+11x^2).
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%I #13 Sep 22 2017 10:01:30

%S 1,4,21,124,761,4724,29421,183404,1143601,7131364,44471301,277325404,

%T 1729418921,10784771924,67254567261,419404046924,2615432135521,

%U 16310012568004,101710347053301,634272638178364,3955367287840601

%N Expansion of (1-4x)/(1-8x+11x^2).

%C Binomial transform of A098648. Second binomial transform of A001077. Third binomial transform of A084057. 4th binomial transform of (1, 0, 5, 0, 25, 0, 125, 0, 625, 0, 3125, ...).

%H Seiichi Manyama, <a href="/A108404/b108404.txt">Table of n, a(n) for n = 0..1258</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-11).

%F E.g.f.: exp(4x)cosh(sqrt(5)x).

%F a(n) = 8a(n-1) - 11a(n-2), a(0) = 1, a(1) = 4.

%F a(n) = ((4+sqrt(5))^n + (4-sqrt(5))^n)/2.

%F a(n+1)/a(n) converges to 4 + sqrt(5) = 6.2360679774997896964... = 4+A002163.

%F a(n) = A091870(n+1)-4*A091870(n). - _R. J. Mathar_, Nov 10 2013

%t CoefficientList[Series[(1-4x)/(1-8x+11x^2),{x,0,30}],x] (* or *) LinearRecurrence[{8,-11},{1,4},30] (* _Harvey P. Dale_, Jan 03 2012 *)

%Y Cf. A001077, A084057, A098648.

%K easy,nonn

%O 0,2

%A _Philippe Deléham_, Jul 04 2005