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A001020 Powers of 11.
(Formerly M4807 N2054)
61

%I M4807 N2054

%S 1,11,121,1331,14641,161051,1771561,19487171,214358881,2357947691,

%T 25937424601,285311670611,3138428376721,34522712143931,

%U 379749833583241,4177248169415651,45949729863572161,505447028499293771,5559917313492231481,61159090448414546291

%N Powers of 11.

%C The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n>=1, a(n) equals the number of 11-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011

%C a(n), for n <= 4, gives the n-th row of Pascals' triangle (A007318); a(n), n >= 5 "sort of" gives the n-th row of Pascals' triangle, but now the binomial coefficients with more than one digit overlap. - _Daniel Forgues_, Aug 12 2012

%C Numbers n such that sigma(11*n) = 11*n + sigma(n). - _Jahangeer Kholdi_, Nov 13 2013

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H T. D. Noe, <a href="/A001020/b001020.txt">Table of n, a(n) for n = 0..100</a>

%H P. J. Cameron, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL3/groups.html">Sequences realized by oligomorphic permutation groups</a>, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=275">Encyclopedia of Combinatorial Structures 275</a>

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

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/MasterThesis.pdf">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992.

%H Simon Plouffe, <a href="http://www.lacim.uqam.ca/%7Eplouffe/articles/FonctionsGeneratrices.pdf">1031 Generating Functions and Conjectures</a>, Université du Québec à Montréal, 1992.

%H Y. Puri and T. Ward, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL4/WARD/short.html">Arithmetic and growth of periodic orbits</a>, J. Integer Seqs., Vol. 4 (2001), #01.2.1.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (11).

%F G.f.: 1/(1-11*x).

%F E.g.f.: exp(11*x).

%F a(n) = 11*a(n-1), n>0 ; a(0)=1. - _Philippe Deléham_, Nov 23 2008

%p A001020:=-1/(-1+11*z); [_Simon Plouffe_ in his 1992 dissertation.]

%t Table[11^n,{n,0,40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011 *)

%o (MAGMA) [11^n: n in [0..100]]; // _Vincenzo Librandi_, Apr 24 2011

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

%o (PARI) a(n)=n^11 \\ _Charles R Greathouse IV_, Sep 24 2015

%Y Cf. A096884, A097659, A007318.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified February 17 19:37 EST 2019. Contains 320223 sequences. (Running on oeis4.)