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%I #79 Sep 08 2022 08:44:32
%S 1,10,90,810,7290,65610,590490,5314410,47829690,430467210,3874204890,
%T 34867844010,313810596090,2824295364810,25418658283290,
%U 228767924549610,2058911320946490,18530201888518410,166771816996665690,1500946352969991210,13508517176729920890
%N Expansion of g.f.: (1+x)/(1-9*x).
%C Coordination sequence for infinite tree with valency 10.
%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 Except 1, all terms are in A033583. - _Vincenzo Librandi_, May 26 2014
%C For n>=1, a(n) equals the number of words of length n on alphabet {0,1,...,9} with no two adjacent letters identical. - _Milan Janjic_, Jan 31 2015 [Corrected by _David Nacin_, May 31 2017]
%C a(n) is the number of sequences over the alphabet {0,1,...,9} of length n such that no two consecutive terms have distance 5. - _David Nacin_, May 31 2017
%H Vincenzo Librandi, <a href="/A003952/b003952.txt">Table of n, a(n) for n = 0..1000</a>
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=311">Encyclopedia of Combinatorial Structures 311</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 (9).
%H <a href="/index/Tra#trees">Index entries for sequences related to trees</a>
%F a(n) = (10*9^n - 0^n)/9. Binomial transform is A000042. - _Paul Barry_, Jan 29 2004
%F G.f.: (1+x)/(1-9*x). - _Philippe Deléham_, Jan 31 2004
%F a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 8. - _Philippe Deléham_, Jul 10 2005
%F The Hankel transform of this sequence is: [1,-10,0,0,0,0,0,0,0,...]. - _Philippe Deléham_, Nov 21 2007
%F E.g.f.: (10*exp(9*x) - 1)/9. - _G. C. Greubel_, Sep 24 2019
%p k:= 10; seq(`if`(n = 0, 1, k*(k-1)^(n-1)), n = 0..20); # modified by _G. C. Greubel_, Sep 24 2019
%t Join[{1}, 10*9^Range[0, 25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 11 2011 *)
%t Join[{1},NestList[9#&,10,20]] (* _Harvey P. Dale_, Sep 01 2021 *)
%o (Magma) [(10*9^n-0^n)/9: n in [0..20] ]; // _Vincenzo Librandi_, Aug 19 2011
%o (PARI) a(n)=10*9^n\9 \\ _Charles R Greathouse IV_, Sep 08 2011
%o (Sage) k=10; [1]+[k*(k-1)^(n-1) for n in (1..20)] # _G. C. Greubel_, Sep 24 2019
%o (GAP) k:=10;; Concatenation([1], List([1..20], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 24 2019
%Y Cf. A003949, A003950, A003951.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Mar 15 1996
%E Edited by _N. J. A. Sloane_, Dec 04 2009
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