A008593 - OEIS

%I #71 Jan 06 2025 03:09:12

%S 0,11,22,33,44,55,66,77,88,99,110,121,132,143,154,165,176,187,198,209,

%T 220,231,242,253,264,275,286,297,308,319,330,341,352,363,374,385,396,

%U 407,418,429,440,451,462,473,484,495,506,517,528,539,550,561,572,583

%N Multiples of 11.

%C 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

%C 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

%H Vincenzo Librandi, <a href="/A008593/b008593.txt">Table of n, a(n) for n = 0..10000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=323">Encyclopedia of Combinatorial Structures 323</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H Luis Manuel Rivera, <a href="http://arxiv.org/abs/1406.3081">Integer sequences and k-commuting permutations</a>, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 11*n.

%F G.f.: 11*x/(1-x)^2. - _David Wilding_, Jun 21 2014

%F E.g.f.: 11*x*exp(x). - _Stefano Spezia_, Oct 08 2022

%p 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

%t Range[0, 1000, 11] (* _Vladimir Joseph Stephan Orlovsky_, May 28 2011 *)

%o (Magma) [11*n: n in [0..60]]; // _Vincenzo Librandi_, Sep 18 2011

%o (Maxima) makelist(11*n,n,0,20); /* _Martin Ettl_, Dec 17 2012 */

%o (Haskell)

%o a008593 = (* 11)

%o a008593_list = [0, 11 ..]  -- _Reinhard Zumkeller_, Jul 05 2014

%o (PARI) a(n)=11*n \\ _Charles R Greathouse IV_, Nov 06 2014

%Y Cf. A008591, A008592, A059632; union of A135499 and A060979.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_