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%I A164038 #20 Mar 17 2024 02:12:11
%S A164038 5,31,195,1237,7885,50399,322635,2067173,13251125,84966271,544886835,
%T A164038 3494644117,22414043965,143763624959,922113238395,5914569009893,
%U A164038 37937085615845,243335768930911,1560804720144675,10011324516035797
%N A164038 Expansion of (5-19*x)/(1-10*x+23*x^2).
%C A164038 Binomial transform of A161731 without initial 1. Fifth binomial transform of A164095. Inverse binomial transform of A164110.
%H A164038 G. C. Greubel, <a href="/A164038/b164038.txt">Table of n, a(n) for n = 0..1000</a> (terms 0..100 from Vincenzo Librandi)
%H A164038 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).
%F A164038 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 31.
%F A164038 G.f.: (5-19*x)/(1-10*x+23*x^2).
%F A164038 a(n) = ((5+3*sqrt(2))*(5+sqrt(2))^n + (5-3*sqrt(2))*(5-sqrt(2))^n)/2.
%F A164038 E.g.f: (5*cosh(sqrt(2)*x) + 3*sqrt(2)*sinh(sqrt(2)*x))*exp(5*x). - _G. C. Greubel_, Sep 08 2017
%t A164038 LinearRecurrence[{10,-23},{5,31},50] (* or *) CoefficientList[Series[(5 - 19*x)/(1 - 10*x + 23*x^2), {x,0,50}], x] (* _G. C. Greubel_, Sep 08 2017 *)
%o A164038 (Magma) Z<x>:= PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+3*r)*(5+r)^n+(5-3*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 10 2009
%o A164038 (PARI) Vec((5-19*x)/(1-10*x+23*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Sep 26 2012
%Y A164038 Cf. A161731, A164095, A164110.
%K A164038 nonn,easy
%O A164038 0,1
%A A164038 Al Hakanson (hawkuu(AT)gmail.com), Aug 08 2009
%E A164038 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 10 2009

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