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 A003954 #61 Mar 25 2025 17:58:55
%S A003954 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,
%T A003954 28295372292,311249095212,3423740047332,37661140520652,
%U A003954 414272545727172,4556998002998892,50126978032987812,551396758362865932,6065364341991525252,66719007761906777772,733909085380974555492
%N A003954 Expansion of g.f.: (1+x)/(1-11*x).
%C A003954 Coordination sequence for infinite tree with valency 12.
%C A003954 The n-th term of the coordination sequence of the infinite tree with valency 2m is the same as the number of reduced words of size n in the free group on m generators. In the five sequences A003946, A003948, A003950, A003952, A003954 m is 2, 3, 4, 5, 6 . - Avi Peretz (njk(AT)netvision.net.il), Feb 23 2001 and Ola Veshta (olaveshta(AT)my-deja.com), Mar 30 2001.
%C A003954 For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,11} with no two adjacent letters identical. - _Milan Janjic_, Jan 31 2015
%H A003954 Vincenzo Librandi, <a href="/A003954/b003954.txt">Table of n, a(n) for n = 0..900</a>
%H A003954 INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=313">Encyclopedia of Combinatorial Structures 313</a>.
%H A003954 <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%H A003954 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (11).
%H A003954 <a href="/index/Tra#trees">Index entries for sequences related to trees</a>.
%F A003954 a(n) = Sum_{k=0..n} A029653(n,k)*x^k for x = 10. - _Philippe Deléham_, Jul 10 2005
%F A003954 G.f.: (1+x)/(1-11*x). The Hankel transform of this sequence is [1,-12,0,0,0,0,0,0,0,...]. - _Philippe Deléham_, Nov 21 2007
%F A003954 a(0) = 1; for n>0, a(n) = 12*11^(n-1). - _Vincenzo Librandi_, Nov 18 2010
%F A003954 a(0) = 1, a(1)=12, a(n) = 11*a(n-1). - _Vincenzo Librandi_, Dec 10 2012
%F A003954 E.g.f.: (12*exp(11*x) - 1)/11. - _Elmo R. Oliveira_, Mar 24 2025
%p A003954 k:=12; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by _G. C. Greubel_, Sep 24 2019
%t A003954 Join[{1}, 12*11^Range[0, 25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 11 2011 *)
%t A003954 CoefficientList[Series[(1+x)/(1-11x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 10 2012 *)
%o A003954 (Magma) [1] cat [12*11^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Dec 11 2012
%o A003954 (PARI) a(n)=12*11^n\11 \\ _Charles R Greathouse IV_, Aug 14 2015
%o A003954 (Sage) [1]+[12*11^(n-1) for n in (1..20)] # _G. C. Greubel_, Sep 23 2019
%o A003954 (GAP) Concatenation([1], List([1..20], n-> 12*11^(n-1) )); # _G. C. Greubel_, Sep 23 2019
%Y A003954 Cf. A003946, A003948, A003950, A003952, A003953, A003954, A029653.
%K A003954 nonn,easy
%O A003954 0,2
%A A003954 _N. J. A. Sloane_
%E A003954 Edited by _N. J. A. Sloane_, Dec 04 2009