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%I M5055 N2186 #38 Mar 07 2024 13:04:53
%S 18,45,69,96,120,147,171,198,222,249,273,300,324,351,375,402,426,453,
%T 477,504,528,555,579,606,630,657,681,708,732,759,783,810,834,861,885,
%U 912,936,963,987,1014,1038,1065,1089
%N a(n) = a(n-1)+a(n-2)-a(n-3).
%C The old defition was a(n) = a(n-2)+a(n-3)-a(n-5).
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H 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 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 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 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 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1, 1, -1).
%F a(n) = 6*A007310(n) + 3*A047208(n).
%p A002798:=3*(6+9*z+2*z**2)/(z+1)/(z-1)**2; # _Simon Plouffe_ in his 1992 dissertation
%t LinearRecurrence[{1,1,-1},{18,45,69},50] (* _Harvey P. Dale_, Sep 17 2023 *)
%Y Cf. A007310, A047208.
%K nonn
%O 1,1
%A _N. J. A. Sloane_, _Simon Plouffe_
%E Definition simplified by _Ray Chandler_. - _N. J. A. Sloane_, Mar 07 2024
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