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A256429 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.

%I A256429 #10 Mar 29 2015 11:32:25
%S A256429 1,6,11,16,41,106,211,416,941,2106,4411,9316,20341,44106,94111,201716,
%T A256429 435741,938606,2014311,4330116,9324641,20060606,43122511,92747016,
%U A256429 199552041,429222606,923076211,1985467416,4270895441,9186237106,19758020411,42498043816,91411232341
%N A256429 a(n) is the total number of pentagrams in a variant of pentagram fractal after n iterations.
%C A256429 Inspired by A255870. But at the higher iterations, the perimeter would be a pentagram instead of a pentagon. See illustration in the links.
%H A256429 Kival Ngaokrajang, <a href="/A256429/a256429.pdf">Illustration of initial terms</a>, <a href="/A256429/a256429_1.pdf">Illustration of n = 6</a>
%F A256429 Conjectures from _Colin Barker_, Mar 29 2015: (Start)
%F A256429 a(n) = 3*a(n-1)-4*a(n-2)+7*a(n-3)-5*a(n-4) for n>3.
%F A256429 G.f.: -(3*x^2-3*x-1) / ((x-1)*(5*x^3-2*x^2+2*x-1)).
%F A256429 (End)
%o A256429 (Small Basic)
%o A256429 a[1]=1
%o A256429 a[2]=0
%o A256429 a[3]=0
%o A256429 a[4]=4
%o A256429 TextWindow.Write("1, 6, 11, 16, 41, ")
%o A256429 b=0
%o A256429 s=41
%o A256429 rs=5
%o A256429 For n=5 To 50
%o A256429   b=b+a[n-4]
%o A256429   a[n]=4*(2*b+3*(a[n-3]/4))
%o A256429   rs=rs+a[n]
%o A256429   s=s+5*rs
%o A256429   TextWindow.Write(s+", ")
%o A256429 EndFor
%Y A256429 Cf. A255870.
%K A256429 nonn
%O A256429 0,2
%A A256429 _Kival Ngaokrajang_, Mar 28 2015