This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A026551 #32 Sep 28 2022 03:54:48
%S A026551 3,9,21,57,129,345,777,2073,4665,12441,27993,74649,167961,447897,
%T A026551 1007769,2687385,6046617,16124313,36279705,96745881,217678233,
%U A026551 580475289,1306069401,3482851737,7836416409,20897110425,47018498457
%N A026551 Expansion of 3*(1+2*x-2*x^2)/((1-x)*(1-6*x^2)).
%C A026551 The even terms are the number of holes of Sierpiński triangle-like fractals. The odd terms are the total number of holes and triangles. - _Kival Ngaokrajang_, Mar 30 2014
%C A026551 All terms are divisible by 3 (see g.f.). - _Joerg Arndt_, Dec 20 2014
%C A026551 Former title a(n) = Sum_{j=0..2*n} Sum_{k=0..j} A026536(j, k) was incorrect. - _G. C. Greubel_, Apr 12 2022
%H A026551 G. C. Greubel, <a href="/A026551/b026551.txt">Table of n, a(n) for n = 0..1000</a>
%H A026551 Kival Ngaokrajang, <a href="/A026551/a026551.pdf">Illustration of initial terms</a>
%H A026551 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 6, -6).
%F A026551 G.f.: 3*(1+2*x-2*x^2)/((1-x)*(1-6*x^2)). - _Ralf Stephan_, Feb 03 2004
%F A026551 From _G. C. Greubel_, Apr 12 2022: (Start)
%F A026551 a(n) = (3/5)*( -1 + 3*6^(n/2)*(1 + (-1)^n) + 8*6^((n-1)/2)*(1 - (-1)^n) ).
%F A026551 a(2*n) = (3/5)*(6^(n+1) - 1).
%F A026551 a(2*n+1) = (3/5)*(16*6^n -1).
%F A026551 a(n) = a(n-1) + 6*a(n-2) - a(n-3). (End)
%t A026551 Table[(3/5)*(-1 +3*6^(n/2)*(1+(-1)^n) +8*6^((n-1)/2)*(1-(-1)^n)), {n, 0, 40}] (* _G. C. Greubel_, Apr 12 2022 *)
%o A026551 (PARI) Vec( 3*(1+2*x-2*x^2)/((1-x)*(1-6*x^2))+O(x^33)); \\ _Joerg Arndt_, Dec 20 2014
%o A026551 (Magma) [(3/5)*(-1 + 6^(1+Floor(n/2))*((n+1) mod 2) + 16*6^(Floor((n-1)/2))*(n mod 2)): n in [0..40]]; // _G. C. Greubel_, Apr 12 2022
%o A026551 (SageMath) [(3/5)*(-1 + 6*6^(n/2)*((n+1)%2) + 16*6^((n-1)/2)*(n%2)) for n in (0..40)] # _G. C. Greubel_, Apr 12 2022
%Y A026551 Cf. A026534, A026565.
%K A026551 nonn,easy
%O A026551 0,1
%A A026551 _Clark Kimberling_
%E A026551 Name corrected by _G. C. Greubel_, Apr 12 2022