cp's OEIS Frontend

A164538 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.

%I A164538 #19 Sep 08 2022 08:45:47
%S A164538 5,33,215,1391,8965,57657,370375,2377639,15257765,97891953,627990935,
%T A164538 4028394431,25840152805,165748456137,1063161046855,6819395977399,
%U A164538 43741255696325,280566449483073,1799615613815255,11543127800041871
%N A164538 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
%C A164538 Binomial transform of A164537. Fifth binomial transform of A164682.
%H A164538 Vincenzo Librandi, <a href="/A164538/b164538.txt">Table of n, a(n) for n = 0..151</a>
%H A164538 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-23).
%F A164538 a(n) = 10*a(n-1) - 23*a(n-2) for n > 1; a(0) = 5, a(1) = 33.
%F A164538 G.f.: (5-17*x)/(1-10*x+23*x^2).
%F A164538 a(n) = ((5+4*sqrt(2))*(5+sqrt(2))^n + (5-4*sqrt(2))*(5-sqrt(2))^n)/2.
%t A164538 LinearRecurrence[{10,-23},{5,33},20] (* _Harvey P. Dale_, May 29 2019 *)
%o A164538 (Magma) Z<x>:=PolynomialRing(Integers()); N<r>:=NumberField(x^2-2); S:=[ ((5+4*r)*(5+r)^n+(5-4*r)*(5-r)^n)/2: n in [0..19] ]; [ Integers()!S[j]: j in [1..#S] ]; // _Klaus Brockhaus_, Aug 21 2009
%o A164538 (PARI) Vec((5-17*x)/(1-10*x+23*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jun 14 2011
%Y A164538 Cf. A164537, A164682.
%K A164538 nonn,easy
%O A164538 0,1
%A A164538 Al Hakanson (hawkuu(AT)gmail.com), Aug 15 2009
%E A164538 Edited and extended beyond a(5) by _Klaus Brockhaus_, Aug 21 2009