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%I #35 Sep 08 2022 08:45:49
%S 1,14,182,2366,30758,399854,5198102,67575326,878479238,11420230094,
%T 148462991222,1930018885886,25090245516518,326173191714734,
%U 4240251492291542,55123269399790046,716602502197270598,9315832528564517774,121105822871338731062,1574375697327403503806
%N Expansion of g.f.: (1+x)/(1-13*x).
%C For n>=1, a(n) equals the numbers of words of length n-1 on alphabet {0,1,...,13} with no two adjacent letters identical. - _Milan Janjic_, Jan 31 2015
%H Vincenzo Librandi, <a href="/A170733/b170733.txt">Table of n, a(n) for n = 0..900</a>
%H M. Janjic, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Janjic/janjic63.html">On Linear Recurrence Equations Arising from Compositions of Positive Integers</a>, J. Int. Seq. 18 (2015) # 15.4.7.
%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (13).
%F a(n) = Sum_{k=0..n} A097805(n,k)*(-1)^(n-k)*14^k. - _Philippe Deléham_, Dec 04 2009
%F a(0) = 1; for n>0, a(n) = 14*13^(n-1). - _Vincenzo Librandi_, Dec 05 2009
%F a(0)=1, a(1)=14, a(n) = 13*a(n-1). - _Vincenzo Librandi_, Dec 10 2012
%F E.g.f.: (14*exp(13*x) - 1)/13. - _G. C. Greubel_, Sep 24 2019
%p k:=14; seq(`if`(n=0, 1, k*(k-1)^(n-1)), n = 0..25); # _G. C. Greubel_, Sep 24 2019
%t Join[{1}, 14*13^Range[0, 25]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 11 2011 *)
%t CoefficientList[Series[(1+x)/(1-13x), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 10 2012 *)
%t Join[{1},NestList[13#&,14,20]] (* _Harvey P. Dale_, Oct 09 2017 *)
%o (PARI) vector(26, n, k=14; if(n==1, 1, k*(k-1)^(n-2))) \\ _G. C. Greubel_, Sep 24 2019
%o (Magma) k:=14; [1] cat [k*(k-1)^(n-1): n in [1..25]]; // _G. C. Greubel_, Sep 24 2019
%o (Sage) k=14; [1]+[k*(k-1)^(n-1) for n in (1..25)] # _G. C. Greubel_, Sep 24 2019
%o (GAP) k:=14;; Concatenation([1], List([1..25], n-> k*(k-1)^(n-1) )); # _G. C. Greubel_, Sep 24 2019
%Y Cf. A003945, A003954, A170732.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_, Dec 04 2009
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