A008593 Multiples of 11.

0, 11, 22, 33, 44, 55, 66, 77, 88, 99, 110, 121, 132, 143, 154, 165, 176, 187, 198, 209, 220, 231, 242, 253, 264, 275, 286, 297, 308, 319, 330, 341, 352, 363, 374, 385, 396, 407, 418, 429, 440, 451, 462, 473, 484, 495, 506, 517, 528, 539, 550, 561, 572, 583

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Numbers for which the sum of "digits" in base 100 is divisible by 11. For instance, 193517302 gives 1 + 93 + 51 + 73 + 02 = 220, and 2 + 20 = 22 = 2 * 11. - Daniel Forgues, Feb 22 2016

Numbers in which the sum of the digits in the even positions equals the sum of the digits in the odd positions. - Stefano Spezia, Jan 05 2025

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 323.
• Tanya Khovanova, Recursive Sequences.
• 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. A008591, A008592, A008604, A059632; union of A135499 and A060979.

Programs

Haskell

a008593 = (* 11)
a008593_list = [0, 11 ..]  -- Reinhard Zumkeller, Jul 05 2014

Magma

[11*n: n in [0..60]]; // Vincenzo Librandi, Sep 18 2011

Maple

g:=(1+10*z)/((1-z)): gser:=series(g, z=0, 88): seq((coeff(gser, z, n))*n, n=0..77); # Zerinvary Lajos, Feb 25 2009

Mathematica

Range[0, 1000, 11] (* Vladimir Joseph Stephan Orlovsky, May 28 2011 *)

Maxima

makelist(11*n,n,0,20); /* Martin Ettl, Dec 17 2012 */

PARI

a(n)=11*n \\ Charles R Greathouse IV, Nov 06 2014

Formula

a(n) = 11*n.

G.f.: 11*x/(1-x)^2. - David Wilding, Jun 21 2014

E.g.f.: 11*x*exp(x). - Stefano Spezia, Oct 08 2022

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

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

a(n) = A008604(n)/2. (End)