cp's OEIS Frontend

A163415 a(n) = 18*a(n-1) - 79*a(n-2) for n>1, a(0)=1, a(1)=13.

%I A163415 #11 Jun 30 2023 00:57:57
%S A163415 1,13,155,1763,19489,211525,2267819,24110267,254827105,2682176797,
%T A163415 28147841051,294769171955,3082165652161,32192217154453,
%U A163415 335968822259435,3504253645468043,36535028659929409,380794477886753965
%N A163415 a(n) = 18*a(n-1) - 79*a(n-2) for n>1, a(0)=1, a(1)=13.
%C A163415 Binomial transform of A163414. Inverse binomial transform of A163416.
%H A163415 G. C. Greubel, <a href="/A163415/b163415.txt">Table of n, a(n) for n = 0..999</a>
%H A163415 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18, -79).
%F A163415 a(n) = ((1+2*sqrt(2))*(9+sqrt(2))^n + (1-2*sqrt(2))*(9-sqrt(2))^n)/2.
%F A163415 G.f.: (1-5*x)/(1-18*x+79*x^2).
%F A163415 E.g.f.: exp(9*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 21 2016
%t A163415 LinearRecurrence[{18,-79}, {1,13}, 50] (* _G. C. Greubel_, Dec 21 2016 *)
%o A163415 (Magma) [n le 2 select 12*n-11 else 18*Self(n-1)-79*Self(n-2): n in [1..18]];
%o A163415 (PARI) Vec((1-5*x)/(1-18*x+79*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 21 2016
%Y A163415 Cf. A163414, A163416.
%K A163415 nonn,easy
%O A163415 0,2
%A A163415 _Klaus Brockhaus_, Jul 27 2009