A002798 a(n) = a(n-1)+a(n-2)-a(n-3). (Formerly M5055 N2186)

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).

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

Table of n, a(n) for n=1..43.

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

Index entries for linear recurrences with constant coefficients, signature (1, 1, -1).

Formula

a(n) = 6*A007310(n) + 3*A047208(n).

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

Cf. A007310, A047208.

Sequence in context: A095739 A055577 A281917 * A124388 A179896 A075284

Adjacent sequences: A002795 A002796 A002797 * A002799 A002800 A002801

Keyword

nonn

Author

N. J. A. Sloane, Simon Plouffe

Extensions

Definition simplified by Ray Chandler. - N. J. A. Sloane, Mar 07 2024

Status

approved