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%I #15 Nov 12 2018 07:39:54
%S 1,5,14,34,124,260,1016,2056,8176,16400,65504,131104,524224,1048640,
%T 4194176,8388736,33554176,67109120,268434944,536871424,2147482624,
%U 4294968320,17179867136,34359740416,137438949376,274877911040
%N a(n) = 10*a(n-2) - 16*a(n-4) for n > 3, a(0) = 1, a(1) = 5, a(2) = 14, a(3) = 34.
%C a(n)/A083333(n) converges to 3.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 10, 0, -16).
%F G.f.: (1 + 5*x + 4*x^2 - 16*x^3)/(1 - 10*x^2 + 16*x^4).
%F a(n) = A016116(n)*A014551(n+1). - _R. J. Mathar_, Jul 08 2009
%F From _Franck Maminirina Ramaharo_, Nov 12 2018: (Start)
%F a(n) = sqrt(2)^(3*n - 1)*(1 + sqrt(2) + (-1)^n*(sqrt(2) - 1)) + sqrt(2)^(n - 3)*(1 - sqrt(2) - (-1)^n*(sqrt(2) + 1)).
%F E.g.f.: (sinh(sqrt(2)*x) + 2*sinh(2*sqrt(2)*x))/sqrt(2) - cosh(sqrt(2)*x) + 2*cosh(2*sqrt(2)*x). (End)
%t CoefficientList[Series[(1+5x+4x^2-16x^3)/(1-10x^2+16x^4), {x, 0, 30}], x]
%o (Maxima) (a[0] : 1, a[1] : 5, a[2] : 14, a[3] : 34, a[n] := 10*a[n - 2] - 16*a[n - 4], makelist(a[n], n, 0, 50));/* _Franck Maminirina Ramaharo_, Nov 12 2018 */
%Y Cf. A147590, A081342 (bisections). [_R. J. Mathar_, Jul 13 2009]
%Y Cf. A199710. [_Bruno Berselli_, Nov 11 2011]
%K nonn,easy
%O 0,2
%A Mario Catalani (mario.catalani(AT)unito.it), Apr 24 2003
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