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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.
10
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.
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
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Oct 18 2014
EXTENSIONS
Edited. Small changes in the text. - Wolfdieter Lang, Nov 10 2014
STATUS
approved