cp's OEIS Frontend

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.

%I A248969 #9 Nov 10 2014 17:19:50
%S A248969 1,3,6,15,18,42,24,57,30,72,36,87,48,114,54,129,60,144,66,159,78,186,
%T A248969 84,201,90,216,96,231,108,258,114,273,120,288,126,303,138,330,144,345,
%U A248969 150,360,156,375,168,402,174,417,180,432,186,447,198,474,204,489,210,504,216,519
%N 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.
%C A248969 The construction rules alternate between "vertex to vertex" (A061777 & companions) and "side to vertex" (A101946 & companions). See the link for an illustration.
%H A248969 Kival Ngaokrajang, <a href="/A248969/a248969.pdf">Illustration of initial terms</a>
%F A248969 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
%o A248969 (PARI)
%o A248969 {
%o A248969 c2=0;c3=0;c6=3;c7=1;c8=0;
%o A248969 for(n=0,100,
%o A248969    if (Mod(n,2)==0,
%o A248969    \\even
%o A248969        if (n<1,a(n)=1,c3=c3+c2;a=6*c3);
%o A248969        c1=n/8+3/4;
%o A248969        if (c1==floor(c1),c2=2,c2=1)
%o A248969    ,
%o A248969    \\odd
%o A248969        c4=(n^2-1)/16;
%o A248969        if (c4==floor(c4),c5=-1,c5=1);
%o A248969        if (n>4, c6=c6+c5);
%o A248969        if (n>=2, c7=c7+c6);
%o A248969        if (c6<>4, c9=0,c9=2);
%o A248969        a=3*(c7+c8+c9);
%o A248969        c8=c7
%o A248969    );
%o A248969    print1(a", ")
%o A248969 )
%o A248969 }
%Y A248969 Vertex to vertex: A061777, A247618, A247619, A247620.
%Y A248969 Side to side: A101946, A247903, A247904, A247905.
%K A248969 nonn
%O A248969 0,2
%A A248969 _Kival Ngaokrajang_, Oct 18 2014
%E A248969 Edited. Small changes in the text. - _Wolfdieter Lang_, Nov 10 2014