cp's OEIS Frontend

A163413 a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 11.

%I A163413 #10 Jun 30 2023 00:56:22
%S A163413 1,11,107,981,8705,75763,651547,5560797,47228449,399840827,3378034475,
%T A163413 28499963781,240231872609,2023747918819,17041572850843,
%U A163413 143465867727309,1207568224192705,10163059355514347,85527124440143723
%N A163413 a(n) = 14*a(n-1) - 47*a(n-2) for n > 1; a(0) = 1, a(1) = 11.
%C A163413 Binomial transform of A163412. Inverse binomial transform of A163414.
%H A163413 G. C. Greubel, <a href="/A163413/b163413.txt">Table of n, a(n) for n = 0..1000</a>
%H A163413 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14, -47).
%F A163413 a(n) = ((1+2*sqrt(2))*(7+sqrt(2))^n + (1-2*sqrt(2))*(7-sqrt(2))^n)/2.
%F A163413 G.f.: (1-3*x)/(1-14*x+47*x^2).
%F A163413 E.g.f.: exp(7*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 21 2016
%t A163413 LinearRecurrence[{14,-47}, {1,11}, 50] (* _G. C. Greubel_, Dec 21 2016 *)
%o A163413 (Magma) [ n le 2 select 10*n-9 else 14*Self(n-1)-47*Self(n-2): n in [1..19] ];
%o A163413 (PARI) Vec((1-3*x)/(1-14*x+47*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 21 2016
%Y A163413 Cf. A163412, A163414.
%K A163413 nonn,easy
%O A163413 0,2
%A A163413 _Klaus Brockhaus_, Jul 27 2009