This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A187505 #10 Feb 03 2019 16:39:52
%S A187505 0,1,0,1,1,1,2,3,3,6,8,9,17,23,26,49,66,75,141,190,216,406,547,622,
%T A187505 1169,1575,1791,3366,4535,5157,9692,13058,14849,27907,37599,42756,
%U A187505 80355,108262,123111,231373,311728,354484,666212,897585,1020696
%N A187505 Let i be in {1,2,3,4} and let r >= 0 be an integer. Let p = {p_1, p_2, p_3, p_4} = {-1,0,1,2}, n=3*r+p_i, and define a(-1)=0. Then a(n)=a(3*r+p_i) gives the quantity of H_(9,3,0) tiles in a subdivided H_(9,i,r) tile after linear scaling by the factor Q^r, where Q=sqrt(x^3-2*x) with x=2*cos(Pi/9).
%C A187505 (Start) See A187506 for supporting theory. Define the matrix
%C A187505 U_3=
%C A187505 (0 0 0 1)
%C A187505 (0 0 1 1)
%C A187505 (0 1 1 1)
%C A187505 (1 1 1 1).
%C A187505 2. Let r>=0 and M=(m_(i,j))=(U_3)^r, i,j=1,2,3,4. Let C_r be the r-th "block" defined by C_r={a(3*r-1),a(3*r),a(3*r+1),a(3*r+2)} with a(-1)=0. Note that C_r-2*C_(r-1)-3*C_(r-2)+C_(r-3)+C_(r-4)={0,0,0,0}, for r>=4. Let p={p_1,p_2,p_3,p_4}={-1,0,1,2} and n=3*r+p_i. Then a(n)=a(3*r+p_i)=m_(i,3), where M=(m_(i,j))=(U_3)^r was defined above. Hence the block C_r corresponds component-wise to the third column of M, and a(3*r+p_i)=m_(i,3) gives the quantity of H_(9,3,0) tiles that should appear in a subdivided H_(9,i,r) tile. (End)
%C A187505 Since a(3*r+2)=a(3*(r+1)-1) for all r, this sequence arises by concatenation of third-column entries m_(2,3), m_(3,3) and m_(4,3) of M=(U_3)^r.
%F A187505 Recurrence: a(n)=2*a(n-3)+3*a(n-6)-a(n-9)-a(n-12), for n>=12, with initial conditions {a(k)}={0,1,0,1,1,1,2,3,3,6,8,9}, k=0,1,...,11.
%F A187505 G.f.: x*(1+x^2-x^3+x^4-2*x^6+x^7-x^8)/(1-2*x^3-3*x^6+x^9+x^12).
%Y A187505 Cf. A187503, A187504, A187506.
%K A187505 nonn,easy
%O A187505 0,7
%A A187505 _L. Edson Jeffery_, Mar 14 2011