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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. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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

Table of n, a(n) for n=0..59.

Kival Ngaokrajang, Illustration of initial terms

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

PROG

(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", ")

)

}

CROSSREFS

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

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

Cf. A248969.

Sequence in context: A124518 A160724 A212060 * A248969 A174279 A233554

Adjacent sequences:  A249243 A249244 A249245 * A249247 A249248 A249249

KEYWORD

nonn

AUTHOR

Kival Ngaokrajang, Oct 23 2014

EXTENSIONS

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

STATUS

approved

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Last modified June 20 04:43 EDT 2021. Contains 345157 sequences. (Running on oeis4.)