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%I #12 Sep 08 2022 08:45:46
%S 2,11,62,353,2018,11555,66206,379433,2174786,12465659,71453054,
%T 409570865,2347677218,13456996499,77136168158,442148390777,
%U 2534416940162,14527406441195,83271831307454,477318366724097
%N a(n) = ((2+sqrt(3))*(4+sqrt(3))^n + (2-sqrt(3))*(4-sqrt(3))^n)/2.
%C Binomial transform of A162273, inverse binomial transform of A162275.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8, -13).
%F a(n) = 8*a(n-1) - 13*a(n-2) for n > 1; a(0) = 2, a(1) = 11.
%F G.f.: (2-5*x)/(1-8*x+13*x^2).
%p a := proc (n) options operator, arrow; expand((1/2)*(2+sqrt(3))*(4+sqrt(3))^n+(1/2)*(2-sqrt(3))*(4-sqrt(3))^n) end proc: seq(a(n), n = 0 .. 20); # _Emeric Deutsch_, Jul 09 2009
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((2+r)*(4+r)^n+(2-r)*(4-r)^n)/2: n in [0..21] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 05 2009
%Y Cf. A162273, A162275.
%K nonn
%O 0,1
%A Al Hakanson (hawkuu(AT)gmail.com), Jun 29 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 05 2009
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