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Number of frieze patterns of length n under a certain group (see Pisanski et al. for precise definition).
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%I #7 Sep 19 2017 05:39:36

%S 0,1,4,6,23,52,194,586,2131,7286,26524,95326,350738,1290556,4798174,

%T 17895736,67127315,252645136,954510114,3616814566,13744183772,

%U 52357696956,199912348954,764877654106,2932035552786,11258999068468,43303860638644,166799986203766

%N Number of frieze patterns of length n under a certain group (see Pisanski et al. for precise definition).

%H T. Pisanski, D. Schattschneider and B. Servatius, <a href="http://www.jstor.org/stable/27642932">Applying Burnside's lemma to a one-dimensional Escher problem</a>, Math. Mag., 79 (2006), 167-180. See G(n).

%F See Maple program.

%p V:=proc(n) local k, t1; t1:=0; for k in divisors(n) do t1 := t1+phi(k)*4^(n/k); od: t1; end;

%p H:=n-> if n mod 2 = 0 then (n/2)*4^(n/2); else 0; fi;

%p R:=proc(n) local k, t1; t1:=0; for k in divisors(n) do if k mod 2 = 0 then t1 := t1+phi(k)*4^(n/k); fi; od: t1; end;

%p A123046:=n->(V(n)+2*H(n)+R(n))/(4*n);

%K nonn

%O 0,3

%A _N. J. A. Sloane_, Nov 11 2006