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%I #14 Jul 16 2021 16:06:40
%S 1,6,12,136,272,3168,6336,73856,147712,1721856,3443712,40142848,
%T 80285696,935878656,1871757312,21818802176,43637604352,508677193728,
%U 1017354387456,11859151814656,23718303629312,276480808452096
%N Expansion of (1 + 6*x - 12*x^2 - 8*x^3)/(1 - 24*x^2 + 16*x^4).
%C The signed sequence (-1)^C(n+1, 2)*a(n) with g.f. (1 - 6x + 12x^2 - 8x^3) / (1 + 24x^2 + 16x^4) is the Hankel transform of (-1)^C(n+1, 2)*A063886.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,24,0,-16).
%F G.f.: (1 + 6*x - 12*x^2 - 8*x^3)/(1 - 24*x^2 + 16*x^4).
%F a(n) = 2^n*((((3 + 2*sqrt(2))^((n+1)/2) + (3-2*sqrt(2))^((n+1)/2))/2)(1 - (-1)^n)/2 + (((3 + 2*sqrt(2))^(n/2) + (3 - 2*sqrt(2))^(n/2))/2)(1 + (-1)^n)/2).
%t CoefficientList[Series[(1 + 6 x - 12 x^2 - 8 x^3)/(1 - 24 x^2 + 16 x^4), {x, 0, 20}], x] (* _Wesley Ivan Hurt_, Mar 30 2017 *)
%t LinearRecurrence[{0,24,0,-16},{1,6,12,136},30] (* _Harvey P. Dale_, Jul 16 2021 *)
%Y Cf. A063886.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Aug 17 2009
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