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A060919 Number of corners in a 4-sided fractal.

%I A060919 #28 Dec 26 2024 18:11:17
%S A060919 4,8,20,60,204,748,2860,11180,44204,175788,701100,2800300,11193004,
%T A060919 44755628,178989740,715893420,2863442604,11453508268,45813508780,
%U A060919 183252986540,733009849004,2932035201708,11728132418220,46912512895660,187650018028204,750600005003948,3002399885798060
%N A060919 Number of corners in a 4-sided fractal.
%H A060919 Harry J. Smith, <a href="/A060919/b060919.txt">Table of n, a(n) for n=1,...,200</a>
%H A060919 Henry Bottomley, <a href="/A060919/a060919.gif">Illustration of initial terms</a>
%H A060919 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F A060919 a(n) = 4^n/6+2^n+4/3 = (2^n+2)*(2^n+4)/6 = 4*A007581(n-1) = 4(a(n-1)-1)-2^n = A028400(n-1)-A002450(n-1).
%F A060919 From _Colin Barker_, Nov 28 2012: (Start)
%F A060919 a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3).
%F A060919 G.f.: -4*x*(5*x^2-5*x+1) / ((x-1)*(2*x-1)*(4*x-1)). (End)
%F A060919 E.g.f.: (exp(4*x) + 6*exp(2*x) + 8*exp(x) - 15)/6. - _Stefano Spezia_, Dec 26 2024
%t A060919 LinearRecurrence[{7,-14,8},{4,8,20},30] (* _Harvey P. Dale_, Sep 01 2023 *)
%o A060919 (PARI) a(n) = { (2^n + 2)*(2^n + 4)/6 } \\ _Harry J. Smith_, Jul 14 2009
%Y A060919 Cf. A007581, A002450, A028400.
%K A060919 nonn,easy
%O A060919 1,1
%A A060919 _Henry Bottomley_, Apr 10 2001