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Number of palstars of length 2n over an alphabet of size 3.
3

%I #11 Jul 25 2017 02:41:12

%S 1,3,15,81,435,2349,12681,68499,370023,1998945,10798821,58338495,

%T 315162657,1702608147,9198028791,49690672857,268444806483,

%U 1450224181197,7834572084033,42324849273915,228652292458773,1235252381526711,6673226101644267,36050889090859101

%N Number of palstars of length 2n over an alphabet of size 3.

%H Lars Blomberg, <a href="/A246020/b246020.txt">Table of n, a(n) for n = 0..100</a>

%H L. Bruce Richmond and J. Shallit, <a href="http://www.combinatorics.org/ojs/index.php/eljc/article/view/v21i3p25">Counting the Palstars</a>, Electronic Journal of Combinatorics, 21(3) (2014), #P3.25.

%o (PARI) \\ Richmond and Shallit, Section 2

%o U(k,size)= { local u; u= vector(size,x,0); u[1]=1;

%o for (i = 1,length(u)-1,if(i%2==1, u[i+1]=k*u[i], u[i+1]=k*u[i]-u[i\2+1]));

%o return(u); }

%o u = U(3,101);

%o p = vector(length(u),x,0); p[1]=1;

%o for(n=1,length(u)-1,p[n+1]=sum(i=1,n,u[i+1]*p[n-i+1]));

%o p \\ _Lars Blomberg_, Jul 25 2017

%Y Cf, A246019, A246021.

%K nonn

%O 0,2

%A _N. J. A. Sloane_, Aug 13 2014

%E a(11)-a(23) from _Lars Blomberg_, Jul 25 2017