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

0,2

Comments

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

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 +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

Prog

(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", ")
)
}

Crossrefs

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

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

Sequence in context: A160724 A212060 A249246 * A174279 A233554 A276546

Adjacent sequences: A248966 A248967 A248968 * A248970 A248971 A248972

Keyword

nonn

Author

Kival Ngaokrajang, Oct 18 2014

Extensions

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

Status

approved