A261950 - cp's OEIS frontend

A261950 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 "side to vertex" version); for the even n-th generation use the "vertex to vertex" version; a(n) is the number of triangles added in the n-th generation.

%I A261950 #30 Oct 13 2015 13:14:34
%S A261950 1,3,9,12,30,18,45,27,66,33,81,42,102,48,117,57,138,63,153,72,174,78,
%T A261950 189,87,210,93,225,102,246,108,261,117,282,123,297,132,318,138,333,
%U A261950 147,354,153,369,162,390,168,405
%N A261950 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 "side to vertex" version); for the even n-th generation use the "vertex to vertex" version; a(n) is the number of triangles added in the n-th generation.
%C A261950 See a comment on V-V and V-S at A249246.
%C A261950 The overlap rules for the expansion are: (i) overlap within generation is allowed. (ii) overlap of different generations is prohibited.
%C A261950 There are a total of 16 combinations as shown in the table below:
%C A261950 +-------------------------------------------------------+
%C A261950 | Even n-th version    V-V      S-V      V-S      S-S   |
%C A261950 +-------------------------------------------------------+
%C A261950 | Odd n-th  version                                     |
%C A261950 |      V-V           A008486  A248969  A261951  A261952 |
%C A261950 |      S-V             a(n)   A008486  A008486  A261956 |
%C A261950 |      V-S           A249246  A008486  A008486  A261957 |
%C A261950 |      S-S           A261953  A261954  A261955  A008486 |
%C A261950 +-------------------------------------------------------+
%C A261950 Note: V-V = vertex to vertex, S-V = side to vertex,
%C A261950       V-S = vertex to side,  S-S = side to side.
%H A261950 Kival Ngaokrajang, <a href="/A261950/a261950_2.pdf">Illustration of initial terms</a>
%F A261950 Conjectures from _Colin Barker_, Sep 10 2015: (Start)
%F A261950 a(n) = a(n-2)+a(n-4)-a(n-6) for n>6.
%F A261950 G.f.: (7*x^6+3*x^5+20*x^4+9*x^3+8*x^2+3*x+1) / ((x-1)^2*(x+1)^2*(x^2+1)).
%F A261950 (End)
%o A261950 (PARI) {e=9; o=3; print1("1, ", o, ", ", e, ", "); for(n=3, 100, if (Mod(n,2)==0, if (Mod(n,4)==0, e=e+21); if (Mod(n,4)==2, e=e+15); print1(e, ", "), if (Mod(n,4)==3, o=o+9); if (Mod(n,4)==1, o=o+6); print1(o, ", ")))}
%Y A261950 Cf. A008486, A248969, A249246.
%K A261950 nonn
%O A261950 0,2
%A A261950 _Kival Ngaokrajang_, Sep 06 2015
%E A261950 Typo in data fixed by _Colin Barker_, Sep 10 2015

cp's OEIS Frontend