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%I M4807 N2054 #100 Jul 12 2023 12:25:09
%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: a(n) = 11^n.
%C Same as Pisot sequences E(1, 11), L(1, 11), P(1, 11), T(1, 11). Essentially same as Pisot sequences E(11, 121), L(11, 121), P(11, 121), T(11, 121). See A008776 for definitions of Pisot sequences.
%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 Pascal's triangle (A007318); a(n), n >= 5 "sort of" gives the n-th row of Pascal's 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="https://arxiv.org/abs/0911.4975">Approximations de séries génératrices et quelques conjectures</a>, Dissertation, Université du Québec à Montréal, 1992; arXiv:0911.4975 [math.NT], 2009.
%H Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 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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