cp's OEIS Frontend

A163605 a(n) = ((3+2*sqrt(2))*(5+sqrt(2))^n + (3-2*sqrt(2))*(5-sqrt(2))^n)/2.

%I A163605 #7 Sep 08 2022 08:45:46
%S A163605 3,19,121,773,4947,31691,203129,1302397,8352003,53564899,343552921,
%T A163605 2203536533,14133648147,90655141211,581477504729,3729706799437,
%U A163605 23923085385603,153447597468979,984245010820921,6313155366422693
%N A163605 a(n) = ((3+2*sqrt(2))*(5+sqrt(2))^n + (3-2*sqrt(2))*(5-sqrt(2))^n)/2.
%C A163605 Binomial transform of A163604.
%H A163605 G. C. Greubel, <a href="/A163605/b163605.txt">Table of n, a(n) for n = 0..1000</a>
%H A163605 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).
%F A163605 a(n) = 10*a(n-1)-23*a(n-2) for n > 1; a(0) = 3, a(1) = 19.
%F A163605 G.f.: (3-11*x)/(1-10*x+23*x^2).
%F A163605 E.g.f.: exp(5*x)*( 3*cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Jul 29 2017
%t A163605 LinearRecurrence[{10, -23}, {3, 19}, 50] (* _G. C. Greubel_, Jul 29 2017 *)
%o A163605 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((3+2*r)*(5+r)^n+(3-2*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 07 2009
%o A163605 (PARI) x='x+O('x^50); Vec((3-11*x)/(1-10*x+23*x^2)) \\ _G. C. Greubel_, Jul 29 2017
%Y A163605 Cf. A163604.
%K A163605 nonn
%O A163605 0,1
%A A163605 Al Hakanson (hawkuu(AT)gmail.com), Aug 01 2009
%E A163605 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 07 2009