A008602 Multiples of 20.

0, 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300, 320, 340, 360, 380, 400, 420, 440, 460, 480, 500, 520, 540, 560, 580, 600, 620, 640, 660, 680, 700, 720, 740, 760, 780, 800, 820, 840, 860, 880, 900, 920, 940, 960, 980, 1000

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

The multiples of 20 are exactly those integers which do not have a multiple whose decimal digits are of alternating parity. (International Mathematical Olympiad 2004, problem 6, see A110303) - Joseph Myers, Jul 13 2004

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Tanya Khovanova, Recursive Sequences.
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 332.
• Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
• Index entries for linear recurrences with constant coefficients, signature (2,-1).

Crossrefs

Cf. A005843, A008592, A008600, A008601, A110303 (complement), A215145, A317095.

Programs

Mathematica

Range[0, 1500, 20] (* Vladimir Joseph Stephan Orlovsky, Jun 01 2011 *)
CoefficientList[Series[20 x / (x - 1)^2, {x, 0, 60}], x] (* Vincenzo Librandi, Jun 10 2013 *)

PARI

a(n)=20*n \\ Charles R Greathouse IV, Sep 28 2015

Scala

(0 to 1000 by 20).toList // Alonso del Arte, Feb 20 2020

Formula

G.f.: 20*x/(x - 1)^2. - Vincenzo Librandi, Jun 10 2013

E.g.f.: 20*x*exp(x). - Stefano Spezia, Feb 20 2020

From Elmo R. Oliveira, Apr 10 2025: (Start)

a(n) = 20*n = 2*A008592(n) = 10*A005843(n) = A317095(n)/2.

a(n) = 2*a(n-1) - a(n-2). (End)