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%I #29 Sep 08 2022 08:45:11
%S 2,18,56,238,902,3564,13862,54238,211736,827298,3231362,12623044,
%T 49308482,192613698,752401496,2939092798,11480914982,44847668844,
%U 175187526662,684331472398,2673190054136,10442227799538,40790261396162,159338166024964,622419427368002
%N Product of Lucas (A000204) and a Pell Companion series (A002203).
%C Convergent a(n+1)/a(n) = ((1+sqrt(5))/2)*(1+sqrt(2)) = (1.618...)*(2.414213...) = 3.9062796... = (1 + sqrt(2) + sqrt(5) + sqrt(10))/2.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,7,2,-1).
%F a(n) = A000204(n) * A002203(n), n > 0.
%F a(n) = 2*A085292(n).
%F a(n) = (((1+sqrt(5))/2)^n + ((1-sqrt(5))/2)^n) * ((1+sqrt(2))^n + (1-sqrt(2))^n).
%F From _Colin Barker_, Oct 15 2013: (Start)
%F a(n) = 2*a(n-1) + 7*a(n-2) + 2*a(n-3) - a(n-4).
%F G.f.: -2*x*(2*x^3 - 3*x^2 - 7*x - 1) / (x^4 - 2*x^3 - 7*x^2 - 2*x + 1). (End)
%F E.g.f.: 4*(exp(x/2)*(cosh(x/sqrt(2))*cosh(sqrt(5/2)*x)*cosh(sqrt(5)*x/2)+sinh(x/sqrt(2))*sinh(sqrt(5/2)*x)*sinh(sqrt(5)*x/2))-1). - _Stefano Spezia_, Aug 25 2019
%o (Magma) I:=[2,18,56,238]; [n le 4 select I[n] else 2*Self(n-1) + 7*Self(n-2) + 2*Self(n-3) - Self(n-4):n in [1..30]]; // _Marius A. Burtea_, Aug 25 2019
%Y Cf. A000204, A002203, A085292.
%K nonn,easy
%O 1,1
%A _Gary W. Adamson_, Jun 24 2003
%E More terms from _David Wasserman_, Jan 31 2005
%E More terms from _Colin Barker_, Oct 16 2013
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