cp's OEIS Frontend

A249852 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.

%I A249852 #29 Feb 23 2025 11:20:59
%S A249852 0,2,7,14,23,35,50,67,86,108,133,160,189,221,256,293,332,374,419,466,
%T A249852 515,567,622,679,738,800,865,932,1001,1073,1148,1225,1304,1386,1471,
%U A249852 1558,1647,1739,1834,1931,2030,2132,2237,2344,2453,2565,2680,2797,2916,3038,3163,3290,3419
%N A249852 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 A249852 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 A249852 The total pentagons (or pentagrams) after n iterations is A005891. See illustration in the links.
%H A249852 Kival Ngaokrajang, <a href="/A249852/a249852.pdf">Illustration of initial terms</a>
%F A249852 Conjectures from _Colin Barker_, Mar 07 2015: (Start)
%F A249852 a(n) = 3*a(n-1)-4*a(n-2)+4*a(n-3)-3*a(n-4)+a(n-5).
%F A249852 G.f.: -x*(x^3+x^2+x+2) / ((x-1)^3*(x^2+1)). (End)
%F A249852 Conjectured e.g.f.: (exp(x)*(1 + 8*x + 5*x^2) - cos(x) - sin(x))/4. - _Stefano Spezia_, Feb 23 2025
%o A249852 (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 A249852 Cf. A005891, A247619.
%K A249852 nonn
%O A249852 0,2
%A A249852 _Kival Ngaokrajang_, Mar 07 2015