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A002798
a(n) = a(n-1) + a(n-2) - a(n-3).
(Formerly M5055 N2186)
2
18, 45, 69, 96, 120, 147, 171, 198, 222, 249, 273, 300, 324, 351, 375, 402, 426, 453, 477, 504, 528, 555, 579, 606, 630, 657, 681, 708, 732, 759, 783, 810, 834, 861, 885, 912, 936, 963, 987, 1014, 1038, 1065, 1089
OFFSET
1,1
COMMENTS
The old defition was a(n) = a(n-2)+a(n-3)-a(n-5).
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
REFERENCES
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
LINKS
E. Ehrhart, Sur un problème de géométrie diophantienne linéaire I, (Polyèdres et réseaux), J. Reine Angew. Math. 226 1967 1-29. MR0213320 (35 #4184). [Annotated scanned copy of pages 16 and 22 only]
E. Ehrhart, Sur un problème de géométrie diophantienne linéaire II. Systemes diophantiens lineaires, J. Reine Angew. Math. 227 1967 25-49. [Annotated scanned copy of pages 47-49 only]
E. Ehrhart, Sur un problème de géométrie diophantienne linéaire II, (Systèmes diophantiens linéaires), J. Reine Angew. Math. 227 1967 25-49.
Simon Plouffe, Approximations de séries génératrices et quelques conjectures, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
Simon Plouffe, 1031 Generating Functions, Appendix to Thesis, Montreal, 1992
FORMULA
a(n) = 6*A007310(n) + 3*A047208(n).
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
MAPLE
A002798:=3*(6+9*z+2*z**2)/(z+1)/(z-1)**2; # Simon Plouffe in his 1992 dissertation
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {18, 45, 69}, 50] (* Harvey P. Dale, Sep 17 2023 *)
CROSSREFS
Sequence in context: A095739 A055577 A281917 * A124388 A179896 A075284
KEYWORD
nonn
EXTENSIONS
Definition simplified by Ray Chandler. - N. J. A. Sloane, Mar 07 2024
STATUS
approved