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%I #19 Jun 25 2019 11:59:07
%S 1,6,17,47,179,414,1723,3793,16201,35166,151337,327167,1411019,
%T 3046854,13148803,28383073,122510161,264425526,1141401857,2463529487,
%U 10634068259,22951715694,99073772683,213832351153,923033565721
%N a(n) = 12*a(n-2) - 25*a(n-4).
%C a(n)/A083335(n) converges to sqrt(11).
%H Harvey P. Dale, <a href="/A083334/b083334.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,12,0,-25).
%F G.f.: (1 + 6*x + 5*x^2 - 25*x^3) / (1 - 12*x^2 + 25*x^4).
%F a(n) = (x^(n+1) + (-1)^(n+1)*(x-2)^(n+1))/2^ceiling(n/2 + 1) where x = 1 + sqrt(11). - _Ben Paul Thurston_, Aug 30 2006 [edited by _Jon E. Schoenfield_, Jun 25 2019]
%t CoefficientList[Series[(1+6x+5x^2-25x^3)/(1-12x^2+25x^4), {x, 0, 10}], x]
%t LinearRecurrence[{0,12,0,-25},{1,6,17,47},30] (* _Harvey P. Dale_, Oct 15 2012 *)
%K easy,nonn
%O 0,2
%A Mario Catalani (mario.catalani(AT)unito.it), Apr 26 2003
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