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 A002798 M5055 N2186 #49 Apr 02 2025 04:13:26
%S A002798 18,45,69,96,120,147,171,198,222,249,273,300,324,351,375,402,426,453,
%T A002798 477,504,528,555,579,606,630,657,681,708,732,759,783,810,834,861,885,
%U A002798 912,936,963,987,1014,1038,1065,1089
%N A002798 a(n) = a(n-1) + a(n-2) - a(n-3).
%C A002798 The old definition was a(n) = a(n-2)+a(n-3)-a(n-5).
%C A002798 The following applies to this sequence and also to all sequences of the form a(n) = a(n-1) + a(n-2) - a(n-3), regardless of initial values: (a(n+3i) + a(n))/(a(n+2i) + a(n+i)) = 1, as long as a(n+2i) + a(n+i) != 0. - _Klaus Purath_, Jun 05 2024
%D A002798 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A002798 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A002798 E. Ehrhart, <a href="/A002789/a002789.pdf">Sur un problème de géométrie diophantienne linéaire I, (Polyèdres et réseaux)</a>, J. Reine Angew. Math. 226 1967 1-29. MR0213320 (35 #4184). [Annotated scanned copy of pages 16 and 22 only]
%H A002798 E. Ehrhart, <a href="/A002789/a002789_1.pdf">Sur un problème de géométrie diophantienne linéaire II. Systemes diophantiens lineaires</a>, J. Reine Angew. Math. 227 1967 25-49. [Annotated scanned copy of pages 47-49 only]
%H A002798 E. Ehrhart, <a href="http://resolver.sub.uni-goettingen.de/purl?GDZPPN002182424">Sur un problème de géométrie diophantienne linéaire II</a>, (Systèmes diophantiens linéaires), J. Reine Angew. Math. 227 1967 25-49.
%H A002798 Simon Plouffe, <a href="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H A002798 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992.
%H A002798 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A002798 a(n) = 6*A007310(n) + 3*A047208(n).
%F A002798 a(n) = (51*n - 12)/2 - 3*(1 - (-1)^n)/4 = 2*a(n-1) - a(n-2) + 3(-1)^n. - _Klaus Purath_, Jun 05 2024
%p A002798 A002798:=3*(6+9*z+2*z**2)/(z+1)/(z-1)**2; # _Simon Plouffe_ in his 1992 dissertation
%t A002798 LinearRecurrence[{1,1,-1},{18,45,69},50] (* _Harvey P. Dale_, Sep 17 2023 *)
%Y A002798 Cf. A007310, A047208.
%K A002798 nonn
%O A002798 1,1
%A A002798 _N. J. A. Sloane_ and _Simon Plouffe_
%E A002798 Definition simplified by _Ray Chandler_. - _N. J. A. Sloane_, Mar 07 2024