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 A003953 #54 Jul 04 2025 19:01:42
%S A003953 1,11,110,1100,11000,110000,1100000,11000000,110000000,1100000000,
%T A003953 11000000000,110000000000,1100000000000,11000000000000,
%U A003953 110000000000000,1100000000000000,11000000000000000
%N A003953 Expansion of g.f.: (1+x)/(1-10*x).
%C A003953 Coordination sequence for infinite tree with valency 11.
%C A003953 a(n) is sequence A003945(n-1) written in base 2: a(0)=1, a(n) for n >= 1: 2 times 1, (n-1) times 0. a(n) is also A007283(n-1) and A042950(n) for n >= 1 written in base 2. a(n) is also A098011(n+3) and A101229(n+10) for n >= 1 written in base 2. a(n) is also abs(A110164(n+1)) for n >= 1 written in base 2. - _Jaroslav Krizek_, Aug 17 2009
%C A003953 a(n) equals the numbers of words of length n on alphabet {0,1,...,10} with no two adjacent letters identical. - _Milan Janjic_, Jan 31 2015 [Corrected by _David Nacin_, Jun 02 2017]
%H A003953 Vincenzo Librandi, <a href="/A003953/b003953.txt">Table of n, a(n) for n = 0..200</a>
%H A003953 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=312">Encyclopedia of Combinatorial Structures 312</a>
%H A003953 <a href="/index/Di#divseq">Index to divisibility sequences</a>
%H A003953 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (10).
%H A003953 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F A003953 a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 9. - _Philippe Deléham_, Jul 10 2005
%F A003953 G.f.: (1+x)/(1-10*x). - _Paul Barry_, Mar 22 2006
%F A003953 a(0) = 1, a(n) = 10^n + 10^(n-1) = 11*10^(n-1) for n >= 1. - _Jaroslav Krizek_, Aug 17 2009
%F A003953 E.g.f.: (11*exp(10*x) - 1)/10. - _G. C. Greubel_, Sep 24 2019
%p A003953 k:=11; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by _G. C. Greubel_, Sep 24 2019
%t A003953 Join[{1}, 11*10^Range[0, 25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 11 2011 *)
%t A003953 Join[{1},NestList[10#&,11,20]] (* _Harvey P. Dale_, Jul 04 2025 *)
%o A003953 (PARI) a(n)=11*10^n\10 \\ _Charles R Greathouse IV_, Aug 14 2015
%o A003953 (Magma) k:=11; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 24 2019
%o A003953 (Sage) k=11; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019
%o A003953 (GAP) k:=11;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 24 2019
%Y A003953 Cf. A003945, A003952.
%K A003953 nonn,easy
%O A003953 0,2
%A A003953 _N. J. A. Sloane_
%E A003953 Edited by _N. J. A. Sloane_, Dec 04 2009