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A188714 G.f.: (1+x+x^2+x^3)/(1-3*x-3*x^2-3*x^3).

%I A188714 #33 Mar 29 2021 14:11:11
%S A188714 1,4,16,64,252,996,3936,15552,61452,242820,959472,3791232,14980572,
%T A188714 59193828,233896896,924213888,3651913836,14430073860,57018604752,
%U A188714 225301777344,890251367868,3517715249892,13899805185312,54923315409216,217022507533260,857536884383364,3388448121977520,13389022541682432,52905022644129948,209047479923369700
%N A188714 G.f.: (1+x+x^2+x^3)/(1-3*x-3*x^2-3*x^3).
%C A188714 G.f. for number of ways to spin a dreidel n times without having a run of length 4 of any of gimel, heh, nun or shin.
%C A188714 More generally, fix an alphabet of size M and consider the number of words of length n which do not contain M consecutive equal letters. The present sequence is the case M = 4.
%C A188714 For the cases M=2 through 5 see A040000, A121907, A188714, A188680.
%H A188714 Vincenzo Librandi, <a href="/A188714/b188714.txt">Table of n, a(n) for n = 0..1000</a>
%H A188714 J. Noonan and D. Zeilberger, <a href="http://arXiv.org/abs/math.CO/9806036">The Goulden-Jackson cluster method: extensions, applications and implementations</a>
%H A188714 Doron Zeilberger, <a href="http://www.math.rutgers.edu/~zeilberg/gj.html">Webpage of the paper `The Goulden-Jacskon Cluster Method: Extensions, Applications and Implementations', by John Noonan and Doron Zeilberger</a>; <a href="/A188714/a188714.pdf">Local copy, pdf file only, no active links</a>
%H A188714 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3, 3, 3).
%p A188714 # First download the Maple package DAVID_IAN from the Zeilberger web site
%p A188714 read(DAVID_IAN);
%p A188714 M:=4;
%p A188714 lis1:={}; for i from 1 to M do lis1:={op(lis1),x[i]}; od:
%p A188714 lis2:={}; for i from 1 to M do t1:=[]; for j from 1 to M do t1:=[op(t1),x[i]]; od: lis2:={op(lis2),t1}; od:
%p A188714 GJs(lis1, lis2, x);
%t A188714 CoefficientList[Series[(1+x+x^2+x^3)/(1-3x-3x^2-3x^3),{x,0,30}], x]  (* _Harvey P. Dale_, Apr 16 2011 *)
%Y A188714 Cf. A040000, A121907,  A188680. Column 4 of A265624.
%K A188714 nonn
%O A188714 0,2
%A A188714 _N. J. A. Sloane_, Apr 08 2011