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a(n) is the total number of pentagons on the left or the right of the vertical symmetry axis of a pentagon expansion (vertex to vertex) after n iterations.
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%I #26 Mar 18 2015 06:08:37

%S 0,2,7,14,23,35,50,67,86,108,133,160,189,221,256,293,332,374,419,466,

%T 515,567,622,679,738,800,865,932,1001,1073,1148,1225,1304,1386,1471,

%U 1558,1647,1739,1834,1931,2030,2132,2237,2344,2453,2565,2680,2797,2916,3038,3163,3290,3419

%N a(n) is the total number of pentagons on the left or the right of the vertical symmetry axis of a pentagon expansion (vertex to vertex) after n iterations.

%C a(n) is also total number of pentagrams on the left or the right of the vertical symmetry axis of a pentagram expansion (vertex to vertex) after n iterations.

%C The total pentagons (or pentagrams) after n iterations is A005891. See illustration in the links.

%H Kival Ngaokrajang, <a href="/A249852/a249852.pdf">Illustration of initial terms</a>

%F Conjectures from _Colin Barker_, Mar 07 2015: (Start)

%F a(n) = 3*a(n-1)-4*a(n-2)+4*a(n-3)-3*a(n-4)+a(n-5).

%F G.f.: -x*(x^3+x^2+x+2) / ((x-1)^3*(x^2+1)).

%F (End)

%o (PARI) {a=2; s=2; d=2; print1(0,", ",s,", "); for(n=2, 100, if(Mod(n,4)==3, d=2, if(Mod(n,4)==4, d=2, d=3)); a=a+d; s=s+a; print1(s, ", ");)}

%Y Cf. A005891, A247619.

%K nonn

%O 0,2

%A _Kival Ngaokrajang_, Mar 07 2015