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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 (list; graph; refs; listen; history; text; internal format)
 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 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

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Last modified August 8 14:04 EDT 2020. Contains 336298 sequences. (Running on oeis4.)