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.

1, 3, 6, 15, 18, 30, 24, 45, 30, 60, 36, 75, 48, 90, 54, 105, 60, 120, 66, 135, 78, 150, 84, 165, 90, 180, 96, 195, 108, 210, 114, 225, 120, 240, 126, 255, 138, 270, 144, 285, 150, 300, 156, 315, 168, 330, 174, 345, 180, 360, 186, 375, 198, 390, 204, 405, 210, 420, 216, 435

Offset: 0

Author

Kival Ngaokrajang, Oct 23 2014

Keywords

• nonn

Comments

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.

Links

• Kival Ngaokrajang, Illustration of initial terms

Crossrefs

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

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

Cf. A248969.

Programs

PARI

{
c2=0;c3=0;c5=3;
for(n=0,100,
   if (Mod(n,2)==0,
   \\even
       if (n<1,a(n)=1,c3=c3+c2;a=6*c3);
       c1=n/8+3/4;
       if (c1==floor(c1),c2=2,c2=1)
   ,
   \\odd
       a=c5;
       if (n<=1,c4=12,c4=15);
       c5=c5+c4
   );
   print1(a", ")
)
}

Formula

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

Extensions

Edited. Name and comment reformulated. - Wolfdieter Lang, Nov 04 2014