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%I A162558 #10 Jun 30 2023 00:51:54
%S A162558 1,6,38,248,1644,10984,73672,495072,3329936,22407776,150819168,
%T A162558 1015220608,6834184384,46006990464,309717848192,2085024691712,
%U A162558 14036454256896,94493999351296,636137999861248,4282512012883968
%N A162558 a(n) = ((3+sqrt(3))*(5+sqrt(3))^n + (3-sqrt(3))*(5-sqrt(3))^n)/6.
%C A162558 Fifth binomial transform of A108411. Binomial transform of A162557. Inverse binomial transform of A162757.
%C A162558 2nd binomial transform of A086405. - _R. J. Mathar_, Jul 17 2009
%H A162558 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10, -22).
%F A162558 a(n) = 10*a(n-1) - 22*a(n-2) for n > 1; a(0) = 1, a(1) = 6.
%F A162558 G.f.: (1-4*x)/(1-10*x+22*x^2).
%F A162558 From _R. J. Mathar_, Jul 17 2009: (Start)
%F A162558 a(n) = 10*a(n-2) - 22*a(n-2).
%F A162558 G.f.: (1-4*x)/(1-10*x+22*x^2). (End)
%o A162558 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-3); S:=[ ((3+r)*(5+r)^n+(3-r)*(5-r)^n)/6: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 13 2009
%Y A162558 Cf. A108411 (powers of 3 repeated), A162557, A162757.
%K A162558 nonn
%O A162558 0,2
%A A162558 Al Hakanson (hawkuu(AT)gmail.com), Jul 06 2009
%E A162558 Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 13 2009
%E A162558 More terms from _R. J. Mathar_, Jul 17 2009

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