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%I #21 Oct 29 2022 04:49:23
%S 0,2,4,18,56,202,684,2378,8176,28242,97364,335938,1158696,3997082,
%T 13787644,47560698,164059616,565922722,1952143524,6733900658,
%U 23228518936,80126541162,276395677004,953424059818,3288826504656
%N a(n) = 2*A002532(n).
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,5).
%F G.f.: 2*x / (1 - 2*x - 5*x^2).
%F a(n) = 2*a(n-1) + 5*a(n-2), a(0)=0, a(1)=2.
%F a(n) = 1 / sqrt(6) * ( (1+sqrt(6))^n - (1-sqrt(6))^n ).
%F a(n) = 2 * A002533(n-1) + a(n-1).
%t CoefficientList[Series[2x/(1-2x-5x^2), {x, 0, 25}], x]
%t LinearRecurrence[{2,5},{0,2},40] (* _Harvey P. Dale_, Nov 03 2011 *)
%t With[{c=Sqrt[6]}, Simplify/@ Table[((1-c)^n+c (1-c)^n-(1+c)^n+c (1+c)^n)/(5c),{n,30}]] (* _Harvey P. Dale_, Nov 03 2011 *)
%K easy,nonn
%O 0,2
%A Mario Catalani (mario.catalani(AT)unito.it), May 03 2003