A002081 Numbers congruent to {2, 4, 8, 16} (mod 20). (Formerly M1113 N0426)

2, 4, 8, 16, 22, 24, 28, 36, 42, 44, 48, 56, 62, 64, 68, 76, 82, 84, 88, 96, 102, 104, 108, 116, 122, 124, 128, 136, 142, 144, 148, 156, 162, 164, 168, 176, 182, 184, 188, 196, 202, 204, 208, 216, 222, 224, 228, 236, 242, 244, 248, 256, 262, 264, 268, 276, 282

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

Cf. A002082, A008587.

Sequence in context: A334423 A001856 A328265 * A102039 A045844 A254062

Adjacent sequences: A002078 A002079 A002080 * A002082 A002083 A002084

Keyword

nonn,easy,nice

Author

N. J. A. Sloane

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Jul 31 2000

Status

approved