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 A075115 #18 May 02 2025 10:32:01
%S A075115 3,2,0,2,8,12,12,16,32,56,80,112,176,288,448,672,1024,1600,2496,3840,
%T A075115 5888,9088,14080,21760,33536,51712,79872,123392,190464,293888,453632,
%U A075115 700416,1081344,1669120,2576384,3977216,6139904,9478144,14630912
%N A075115 Binomial transform of A073145: a(n)=Sum(binomial(n,k)*A073145(k),(k=0,..,n)).
%C A075115 a(n) is nonnegative since the real root of x^3-2*x^2+2*x-2 is dominant. - _Michael Somos_, Feb 28 2007
%H A075115 Michael De Vlieger, <a href="/A075115/b075115.txt">Table of n, a(n) for n = 0..5303</a>
%H A075115 Yassine Otmani, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL28/Otmani/otmani10.html">The 2-Pascal Triangle and a Related Riordan Array</a>, J. Int. Seq. (2025) Vol. 28, Issue 3, Art. No. 25.3.5. See p. 21.
%H A075115 N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H A075115 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,-2,2).
%F A075115 a(n)=2a(n-1)-2a(n-2)+2a(n-3), a(0)=3, a(1)=2, a(2)=0.
%F A075115 G.f.: (3 - 4*x + 2*x^2)/(1 - 2*x + 2*x^2 - 2*x^3).
%F A075115 a(n) = 3*A077943(n) -4*A077943(n-1) +2*A077943(n-2). - _R. J. Mathar_, Mar 13 2021
%t A075115 CoefficientList[Series[(3-4*x+2*x^2)/(1-2*x+2*x^2-2*x^3), {x, 0, 40}], x]
%t A075115 LinearRecurrence[{2,-2,2},{3,2,0},40] (* _Harvey P. Dale_, Jan 24 2019 *)
%o A075115 (PARI) {a(n)= if(n<0, 0, polsym( x^3 -2*x^2 +2*x -2, n) [n+1])} /* _Michael Somos_, Feb 28 2007 */
%Y A075115 Cf. A073145, A073498.
%K A075115 easy,nonn
%O A075115 0,1
%A A075115 Mario Catalani (mario.catalani(AT)unito.it), Sep 02 2002