%I #13 Sep 08 2022 08:45:39
%S 1,8,73,728,7633,82088,893593,9782648,107374753,1179950408,
%T 12973595113,142680249368,1569336258673,17261966423528,
%U 189877968549433,2088639343496888,22974941225731393,252723895719373448
%N a(n) = (11^n + 5^n)/2.
%C Binomial transform of A081343.
%C Inverse binomial transform of A143079.
%H Vincenzo Librandi, <a href="/A152429/b152429.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-55).
%F a(n) = 16*a(n-1) - 55*a(n-2), with a(0)=1, a(1)=8.
%F G.f.: (1-8*x)/(1 - 16*x + 55*x^2).
%F a(n) = Sum_{k=0..n} A098158(n,k)*8^(2k-n)*9^(n-k).
%F a(n) = ((8 + sqrt(9))^n + (8 - sqrt(9))^n)/2. - Al Hakanson (hawkuu(AT)gmail.com), Dec 08 2008
%F E.g.f.: (exp(11*x) + exp(5*x))/2. - _G. C. Greubel_, Jan 08 2020
%p seq( (11^n+5^n)/2, n=0..20); # _G. C. Greubel_, Jan 08 2020
%t LinearRecurrence[{16,-55}, {1,8}, 20] (* _G. C. Greubel_, Jan 08 2020 *)
%o (Magma) [(11^n+5^n)/2: n in [0..20]]; // _Vincenzo Librandi_, Jun 01 2011
%o (PARI) vector(21, n, (11^(n-1) + 5^(n-1))/2 ) \\ _G. C. Greubel_, Jan 08 2020
%o (Sage) [(11^n+5^n)/2 for n in (0..20)] # _G. C. Greubel_, Jan 08 2020
%o (GAP) List([0..20], n-> (11^n+5^n)/2); # _G. C. Greubel_, Jan 08 2020
%Y Cf. A162516.
%K nonn,less
%O 0,2
%A _Philippe Deléham_, Dec 03 2008