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Start with a single equilateral triangle for n=0; for the odd n-th generation add a triangle at each expandable side of the triangles of the (n-1)-th generation (this is the "vertex to side" version); for the even n-th generation use the "vertex to vertex" version; a(n) is the number of triangles in the n-th generation.
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%I #16 Jan 15 2015 18:40:08

%S 1,3,6,15,18,30,24,45,30,60,36,75,48,90,54,105,60,120,66,135,78,150,

%T 84,165,90,180,96,195,108,210,114,225,120,240,126,255,138,270,144,285,

%U 150,300,156,315,168,330,174,345,180,360,186,375,198,390,204,405,210,420,216,435

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

%C The construction rules alternate between "vertex to side" (A101946 & companions) and "vertex to vertex" (A061777 & companions). 'Vertex to side' means vertex of n-th generation triangle touches the middle of a side of the (n-1)-th generation triangle. See the link with an illustration. The even terms are the same as in A248969. Note that the triangles overlap.

%H Kival Ngaokrajang, <a href="/A249246/a249246.pdf">Illustration of initial terms</a>

%F Empirical g.f.: (3*x^11 + x^10 + 12*x^9 + 5*x^8 + 15*x^7 + 6*x^6 + 15*x^5 + 12*x^4 + 12*x^3 + 5*x^2 + 3*x + 1) / ((x-1)^2*(x+1)^2*(x^2+1)*(x^4+1)). - _Colin Barker_, Oct 24 2014

%o (PARI)

%o {

%o c2=0;c3=0;c5=3;

%o for(n=0,100,

%o if (Mod(n,2)==0,

%o \\even

%o if (n<1,a(n)=1,c3=c3+c2;a=6*c3);

%o c1=n/8+3/4;

%o if (c1==floor(c1),c2=2,c2=1)

%o ,

%o \\odd

%o a=c5;

%o if (n<=1,c4=12,c4=15);

%o c5=c5+c4

%o );

%o print1(a", ")

%o )

%o }

%Y Vertex to vertex: A061777, A247618, A247619, A247620.

%Y Vertex to side: A101946, A247903, A247904, A247905.

%Y Cf. A248969.

%K nonn

%O 0,2

%A _Kival Ngaokrajang_, Oct 23 2014

%E Edited. Name and comment reformulated. - _Wolfdieter Lang_, Nov 04 2014