This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A001022 M4914 N2107 #79 Jul 02 2025 16:01:54
%S A001022 1,13,169,2197,28561,371293,4826809,62748517,815730721,10604499373,
%T A001022 137858491849,1792160394037,23298085122481,302875106592253,
%U A001022 3937376385699289,51185893014090757,665416609183179841,8650415919381337933,112455406951957393129,1461920290375446110677,19004963774880799438801
%N A001022 Powers of 13.
%C A001022 Same as Pisot sequences E(1, 13), L(1, 13), P(1, 13), T(1, 13). Essentially same as Pisot sequences E(13, 169), L(13, 169), P(13, 169), T(13, 169). See A008776 for definitions of Pisot sequences.
%C A001022 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 13-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%C A001022 Numbers n such that sigma(13*n) = 13*n+sigma(n). - _Jahangeer Kholdi_, Nov 23 2013
%D A001022 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A001022 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A001022 T. D. Noe, <a href="/A001022/b001022.txt">Table of n, a(n) for n = 0..100</a>
%H A001022 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 A001022 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=277">Encyclopedia of Combinatorial Structures 277</a>
%H A001022 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A001022 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.
%H A001022 Simon Plouffe, <a href="/A000051/a000051_2.pdf">1031 Generating Functions</a>, Appendix to Thesis, Montreal, 1992
%H A001022 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 A001022 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (13).
%F A001022 G.f.: 1/(1-13*x).
%F A001022 E.g.f.: exp(13*x).
%F A001022 a(n) = 13^n. - _Vincenzo Librandi_, Nov 21 2010
%F A001022 a(n) = 13*a(n-1) n > 0, a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%F A001022 a(n) = Sum_{k=0..n} A001021(k)*binomial(n,k). It is well known that Sum_{k=0..n} (h-1)^k*binomial(n,k) = h^n. - _Bruno Berselli_, Aug 06 2013
%e A001022 For the fifth formula: a(7) = 1*1 + 12*7 + 144*21 + 1728*35 + 20736*35 + 248832*21 + 2985984*7 + 35831808*1 = 62748517. - _Bruno Berselli_, Aug 06 2013
%p A001022 A001022:=-1/(-1+13*z); # _Simon Plouffe_ in his 1992 dissertation
%t A001022 Table[13^n, {n, 0, 40}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 15 2011 *)
%t A001022 13^Range[0,20] (* _Harvey P. Dale_, Jun 16 2024 *)
%o A001022 (Magma) [13^n: n in [0..100]]; // _Vincenzo Librandi_, Nov 21 2010
%o A001022 (Maxima) A001022(n):=13^n$ makelist(A001022(n),n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o A001022 (PARI) first(n)=powers(13,n) \\ _Charles R Greathouse IV_, Jun 17 2021
%Y A001022 Cf. A001021.
%K A001022 nonn,easy
%O A001022 0,2
%A A001022 _N. J. A. Sloane_
%E A001022 More terms from _James Sellers_, Sep 19 2000