|
%I #78 Dec 18 2023 16:23:57
%S 0,5,10,15,20,25,30,35,40,45,50,55,60,65,70,75,80,85,90,95,100,105,
%T 110,115,120,125,130,135,140,145,150,155,160,165,170,175,180,185,190,
%U 195,200,205,210,215,220,225,230,235,240,245,250,255,260,265,270,275
%N Multiples of 5: a(n) = 5 * n.
%C 1/31 = 0.0322580645... = (1/2)^5 + (1/2)^10 + (1/2)^15 + ... - _Gary W. Adamson_, Mar 14 2009
%C Complement of A047201; A079998(a(n))=1; A011558(a(n))=0. - _Reinhard Zumkeller_, Nov 30 2009
%C The y-intercept of a line perpendicular to y=mx,where m is the slope a/b and in this case a=2 and b=1, is a^2 + b^2 or 5, the first value of the list given. The remaining value are multiples of the first number of the list. - _Larry J Zimmermann_, Aug 21 2010
%H Vincenzo Librandi, <a href="/A008587/b008587.txt">Table of n, a(n) for n = 0..1000</a>
%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=317">Encyclopedia of Combinatorial Structures 317</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 From _R. J. Mathar_, May 26 2008: (Start)
%F O.g.f.: 5x/(1-x)^2.
%F a(n) = A008706(n), n > 0.
%F (End)
%F a(n) = Sum_{k>=0} A030308(n,k)*A020714(k). - _Philippe Deléham_, Oct 17 2011
%t Range[0, 500, 5] (* _Vladimir Joseph Stephan Orlovsky_, May 26 2011 *)
%t NestList[#+5&,0,60] (* _Harvey P. Dale_, Dec 18 2023 *)
%o (Maxima) makelist(5*n,n,0,20); /* _Martin Ettl_, Dec 17 2012 */
%o (Magma) [5*n: n in [0..60]]; // _Vincenzo Librandi_, Jun 10 2013
%o (PARI) a(n)=5*n \\ _Charles R Greathouse IV_, Mar 22 2016
%Y Cf. index to numbers of the form n*(d*n+10-d)/2 in A140090.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
|
