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Expansion of g.f.: (1+x)/(1-11*x).
57

%I #57 Sep 08 2022 08:44:32

%S 1,12,132,1452,15972,175692,1932612,21258732,233846052,2572306572,

%T 28295372292,311249095212,3423740047332,37661140520652,

%U 414272545727172,4556998002998892,50126978032987812

%N Expansion of g.f.: (1+x)/(1-11*x).

%C Coordination sequence for infinite tree with valency 12.

%C 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 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 Vincenzo Librandi, <a href="/A003954/b003954.txt">Table of n, a(n) for n = 0..900</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=313">Encyclopedia of Combinatorial Structures 313</a>

%H <a href="/index/Di#divseq">Index to divisibility sequences</a>

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

%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>

%F a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 10. - _Philippe Deléham_, Jul 10 2005

%F 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 a(0) = 1; for n>0, a(n) = 12*11^(n-1). - _Vincenzo Librandi_, Nov 18 2010

%F a(0) = 1, a(1)=12, a(n) = 11*a(n-1). - _Vincenzo Librandi_, Dec 10 2012

%p k:=12; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # modified by _G. C. Greubel_, Sep 24 2019

%t Join[{1}, 12*11^Range[0, 25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 11 2011 *)

%t CoefficientList[Series[(1+x)/(1-11x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 10 2012 *)

%o (Magma) [1] cat [12*11^(n-1): n in [1..20]]; // _Vincenzo Librandi_, Dec 11 2012

%o (PARI) a(n)=12*11^n\11 \\ _Charles R Greathouse IV_, Aug 14 2015

%o (Sage) [1]+[12*11^(n-1) for n in (1..20)] # _G. C. Greubel_, Sep 23 2019

%o (GAP) Concatenation([1], List([1..20], n-> 12*11^(n-1) )); # _G. C. Greubel_, Sep 23 2019

%Y Cf. A003952, A003953.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

%E Edited by _N. J. A. Sloane_, Dec 04 2009