cp's OEIS Frontend

A249246 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.

%I A249246 #16 Jan 15 2015 18:40:08
%S A249246 1,3,6,15,18,30,24,45,30,60,36,75,48,90,54,105,60,120,66,135,78,150,
%T A249246 84,165,90,180,96,195,108,210,114,225,120,240,126,255,138,270,144,285,
%U A249246 150,300,156,315,168,330,174,345,180,360,186,375,198,390,204,405,210,420,216,435
%N A249246 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 A249246 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 A249246 Kival Ngaokrajang, <a href="/A249246/a249246.pdf">Illustration of initial terms</a>
%F A249246 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 A249246 (PARI)
%o A249246 {
%o A249246 c2=0;c3=0;c5=3;
%o A249246 for(n=0,100,
%o A249246    if (Mod(n,2)==0,
%o A249246    \\even
%o A249246        if (n<1,a(n)=1,c3=c3+c2;a=6*c3);
%o A249246        c1=n/8+3/4;
%o A249246        if (c1==floor(c1),c2=2,c2=1)
%o A249246    ,
%o A249246    \\odd
%o A249246        a=c5;
%o A249246        if (n<=1,c4=12,c4=15);
%o A249246        c5=c5+c4
%o A249246    );
%o A249246    print1(a", ")
%o A249246 )
%o A249246 }
%Y A249246 Vertex to vertex: A061777, A247618, A247619, A247620.
%Y A249246 Vertex to side: A101946, A247903, A247904, A247905.
%Y A249246 Cf. A248969.
%K A249246 nonn
%O A249246 0,2
%A A249246 _Kival Ngaokrajang_, Oct 23 2014
%E A249246 Edited. Name and comment reformulated. - _Wolfdieter Lang_, Nov 04 2014