A248969 Start with a single equilateral triangle; at odd n-th generation add a similar triangle at each expandable vertex (this is the "vertex to vertex" version); alternate with the "side to vertex" version for even n-th generation; a(n) is the number of triangle for each generation.

1, 3, 6, 15, 18, 42, 24, 57, 30, 72, 36, 87, 48, 114, 54, 129, 60, 144, 66, 159, 78, 186, 84, 201, 90, 216, 96, 231, 108, 258, 114, 273, 120, 288, 126, 303, 138, 330, 144, 345, 150, 360, 156, 375, 168, 402, 174, 417, 180, 432, 186, 447, 198, 474, 204, 489, 210, 504, 216, 519

Offset: 0

Author

Kival Ngaokrajang, Oct 18 2014

Keywords

• nonn

Comments

The construction rules alternate between "vertex to vertex" (A061777 & companions) and "side to vertex" (A101946 & companions). See the link for an illustration.

Links

• Kival Ngaokrajang, Illustration of initial terms

Crossrefs

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

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

Programs

PARI

{
c2=0;c3=0;c6=3;c7=1;c8=0;
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
       c4=(n^2-1)/16;
       if (c4==floor(c4),c5=-1,c5=1);
       if (n>4, c6=c6+c5);
       if (n>=2, c7=c7+c6);
       if (c6<>4, c9=0,c9=2);
       a=3*(c7+c8+c9);
       c8=c7
   );
   print1(a", ")
)
}

Formula

Empirical g.f.: (3*x^11 +x^10 +12*x^9 +5*x^8 +15*x^7 +6*x^6 +27*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 18 2014

Extensions

Edited. Small changes in the text. - Wolfdieter Lang, Nov 10 2014