OFFSET
0,1
COMMENTS
First differences are periodic, cf. A000689.
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
Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
C. Babbage, On the Determination of the General Term of a New Class of Infinite Series, Trans. Camb. Phil. Soc., 2 (1827), 217-225 (see p. 220).
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 (2,-2,2,-1).
FORMULA
G.f.: 2*(1+2*x^2+2*x^3)/((1-x)^2*(1+x^2)). - Simon Plouffe
a(n+4) = a(n) + 20 for n > 3. - Reinhard Zumkeller, Sep 15 2011
a(n) = 5*n + (1/2)*(3 + (-1)^n)*(-1)^(n(n+1)/2). - Bruno Berselli, Sep 15 2011
E.g.f.: 2*cos(x) - sin(x) + 5*x*exp(x). - Ilya Gutkovskiy, Aug 17 2016
MAPLE
A002081:=2*(1+2*z**2+2*z**3)/(z**2+1)/(z-1)**2; # conjectured by Simon Plouffe in his 1992 dissertation
MATHEMATICA
Flatten[Table[20n + {2, 4, 8, 16}, {n, 0, 14}]] (* Alonso del Arte, Nov 30 2011 *)
LinearRecurrence[{2, -2, 2, -1}, {2, 4, 8, 16}, 57] (* Ray Chandler, Aug 25 2015 *)
Select[Range[300], MemberQ[{2, 4, 8, 16}, Mod[#, 20]]&] (* Harvey P. Dale, Jul 20 2021 *)
PROG
(PARI) a(n) = 5*n + [2, -1, -2, 1][(n%4)+1] \\ Ralf Stephan, Jun 08 2005
(PARI) is(n) = n > 0 && setsearch([2, 4, 8, 16], n%20) > 0 \\ Rick L. Shepherd, Aug 17 2016
(Haskell)
a002081 n = a002081_list
a002081_list = filter ((`elem` [2, 4, 8, 16]) . (`mod` 20)) [1..]
-- Reinhard Zumkeller, Sep 15 2011
CROSSREFS
KEYWORD
nonn,easy,nice
AUTHOR
EXTENSIONS
More terms from Larry Reeves (larryr(AT)acm.org), Jul 31 2000
STATUS
approved