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%I #7 Sep 08 2022 08:45:46
%S 1,9,67,463,3089,20241,131363,848087,5459521,35089209,225323107,
%T 1446179263,9279361169,59531488641,381889579523,2449671556487,
%U 15713255235841,100790106559209,646496195167747,4146789500815663
%N a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
%C Binomial transform of A081180 without initial 0. Fifth binomial transform of A143095.
%H G. C. Greubel, <a href="/A163349/b163349.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).
%F a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
%F a(n) = ((1+2*sqrt(2))*(5+sqrt(2))^n + (1-2*sqrt(2))*(5-sqrt(2))^n)/2.
%F G.f.: (1-x)/(1-10*x+23*x^2).
%F E.g.f.: exp(5*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 19 2016
%t LinearRecurrence[{10,-23}, {1,9}, 50] (* _G. C. Greubel_, Dec 19 2016 *)
%o (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((1+2*r)*(5+r)^n+(1-2*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Jul 26 2009
%o (PARI) Vec((1-x)/(1-10*x+23*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 19 2016
%Y Cf. A081180, A143095.
%K nonn
%O 0,2
%A Al Hakanson (hawkuu(AT)gmail.com), Jul 25 2009
%E Edited and extended beyond a(5) by _Klaus Brockhaus_, Jul 26 2009
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