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%I #12 Nov 03 2016 07:30:31
%S 0,5,25,80,225,605,1600,4205,11025,28880,75625,198005,518400,1357205,
%T 3553225,9302480,24354225,63760205,166926400,437019005,1144130625,
%U 2995372880,7841988025,20530591205,53749785600,140718765605,368406511225,964500768080
%N Related to number of n-circum-C_5 H_5 systems.
%H Colin Barker, <a href="/A122679/b122679.txt">Table of n, a(n) for n = 1..1000</a>
%H J. Brunvoll, S. J. Cyvin and B. N. Cyvin, <a href="http://match.pmf.kg.ac.rs/content34.htm">Azulenoids</a>, MATCH, No. 34, 1996, 91-108.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,1).
%F a(n) = 15*Fibonacci(2*k-1)-5*Fibonacci(2*k)-10 = 5*A004146(n-1).
%F G.f.: -5*x^2*(1+x) / ( (x-1)*(x^2-3*x+1) ). - _R. J. Mathar_, Nov 23 2014
%F a(1)=0, a(2)=5, a(3)=25, a(n) = 4*a(n-1)-4*a(n-2)+a(n-3). - _Harvey P. Dale_, Apr 21 2015
%F a(n) = -5*2^(-1-n)*(2^(2+n)-(3-sqrt(5))^n*(3+sqrt(5))+(-3+sqrt(5))*(3+sqrt(5))^n). - _Colin Barker_, Nov 03 2016
%t LinearRecurrence[{4,-4,1},{0,5,25},40] (* _Harvey P. Dale_, Apr 21 2015 *)
%o (PARI) concat(0, Vec(-5*x^2*(1+x)/((x-1)*(x^2-3*x+1)) + O(x^40))) \\ _Colin Barker_, Nov 03 2016
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_, Sep 23 2006
%E More terms from _Harvey P. Dale_, Apr 21 2015