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 A073717 #25 Oct 08 2024 18:39:25
%S A073717 0,1,4,13,44,149,504,1705,5768,19513,66012,223317,755476,2555757,
%T A073717 8646064,29249425,98950096,334745777,1132436852,3831006429,
%U A073717 12960201916,43844049029,148323355432,501774317241,1697490356184,5742568741225
%N A073717 a(n) = T(2n+1), where T(n) are the tribonacci numbers A000073.
%C A073717 In general, the bisection of a third-order linear recurrence with signature (x,y,z) will result in a third-order recurrence with signature (x^2 + 2*y, 2*z*x - y^2, z^2). - _Gary Detlefs_, May 29 2024
%H A073717 G. C. Greubel, <a href="/A073717/b073717.txt">Table of n, a(n) for n = 0..1000</a>
%H A073717 Meng-Han Wu, Henryk A. Witek, Rafał Podeszwa, <a href="https://match.pmf.kg.ac.rs/electronic_versions/Match93/n2/match93n2_415-462.pdf">Clar Covers and Zhang-Zhang Polynomials of Zigzag and Armchair Carbon Nanotubes</a>, MATCH Commun. Math. Comput. Chem. (2025) Vol. 93, 415-462. See p. 437.
%H A073717 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,1).
%F A073717 a(n) = 3*a(n-1) + a(n-2) + a(n-3), a(0)=0, a(1)=1, a(2)=4.
%F A073717 G.f.: x*(1+x)/(1-3*x-x^2-x^3).
%F A073717 a(n+1) = Sum_{k=0..n} A216182(n,k). - _Philippe Deléham_, Mar 11 2013
%F A073717 a(n) = A113300(n-1) + A113300(n). - _R. J. Mathar_, Jul 04 2019
%t A073717 CoefficientList[Series[(x+x^2)/(1-3x-x^2-x^3), {x, 0, 30}], x]
%t A073717 LinearRecurrence[{3,1,1},{0,1,4},30] (* _Harvey P. Dale_, Sep 07 2015 *)
%o A073717 (Magma) [n le 3 select (n-1)^2 else 3*Self(n-1) +Self(n-2) +Self(n-3): n in [1..31]]; // _G. C. Greubel_, Nov 19 2021
%o A073717 (Sage)
%o A073717 def A073717_list(prec):
%o A073717 P.<x> = PowerSeriesRing(ZZ, prec)
%o A073717 return P( x*(1+x)/(1-3*x-x^2-x^3) ).list()
%o A073717 A073717_list(30) # _G. C. Greubel_, Nov 19 2021
%Y A073717 Cf. A000073, A099463, A113300.
%Y A073717 Row sums of A216182.
%K A073717 easy,nonn
%O A073717 0,3
%A A073717 Mario Catalani (mario.catalani(AT)unito.it), Aug 05 2002