cp's OEIS Frontend

A261951 Start with a single equilateral triangle for n=0; for the odd n-th generation add a triangle at each expandable vertex of the triangles of the (n-1)-th generation (this is the "vertex to vertex" version); for the even n-th generation use the "vertex to side" version; a(n) is the number of triangles added in the n-th generation.

%I A261951 #24 Oct 13 2015 02:26:01
%S A261951 1,3,9,12,24,24,39,27,54,33,69,42,84,54,99,57,114,63,129,72,144,84,
%T A261951 159,87,174,93,189,102,204,114,219,117,234,123,249,132,264,144,279,
%U A261951 147,294,153,309,162,324,174,339,177,354
%N A261951 Start with a single equilateral triangle for n=0; for the odd n-th generation add a triangle at each expandable vertex of the triangles of the (n-1)-th generation (this is the "vertex to vertex" version); for the even n-th generation use the "vertex to side" version; a(n) is the number of triangles added in the n-th generation.
%C A261951 See a comment on V-V and V-S at A249246.
%C A261951 The overlap rules for the expansion are: (i) overlap within generation is allowed. (ii) overlap of different generations is prohibited.
%C A261951 There are a total of 16 combinations as shown in the table below:
%C A261951 +-------------------------------------------------------+
%C A261951 | Even n-th version    V-V      S-V      V-S      S-S   |
%C A261951 +-------------------------------------------------------+
%C A261951 | Odd n-th  version                                     |
%C A261951 |      V-V           A008486  A248969    a(n)   A261952 |
%C A261951 |      S-V           A261950  A008486  A008486  A261956 |
%C A261951 |      V-S           A249246  A008486  A008486  A261957 |
%C A261951 |      S-S           A261953  A261954  A261955  A008486 |
%C A261951 +-------------------------------------------------------+
%C A261951 Note: V-V = vertex to vertex, S-V = side to vertex,
%C A261951       V-S = vertex to side,   S-S = side to side.
%H A261951 Kival Ngaokrajang, <a href="/A261951/a261951.pdf">Illustration of initial terms</a>
%F A261951 Conjectures from _Colin Barker_, Sep 10 2015: (Start)
%F A261951 a(n) = a(n-2)+a(n-8)-a(n-10) for n>10.
%F A261951 G.f.: (7*x^10+3*x^9+14*x^8+3*x^7+15*x^6+12*x^5+15*x^4+9*x^3+8*x^2+3*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)*(x^4+1)).
%F A261951 (End)
%o A261951 (PARI) {e=9; o=3; print1("1, ", o, ", ", e, ", "); for(n=3, 100, if (Mod(n,2)==0, e=e+15; print1(e, ", "), if (Mod(n,8)==3, o=o+9); if (Mod(n,8)==5, o=o+12); if (Mod(n,8)==7, o=o+3); if (Mod(n,8)==1, o=o+6); print1(o, ", ")))}
%Y A261951 Cf. A008486, A248969, A249246.
%K A261951 nonn
%O A261951 0,2
%A A261951 _Kival Ngaokrajang_, Sep 06 2015