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Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A089851/A089853.
6

%I #6 Mar 31 2012 14:02:17

%S 1,1,2,2,5,15,42,132,431,1430,4862,16801,58786,208012,742914,2674440,

%T 9694845,35357712,129644790,477638700,1767263322,6564120420,

%U 24466267020,91482564069,343059613650,1289904147324,4861946402882,18367353072152

%N Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A089851/A089853.

%C The number of n-node binary trees fixed by the corresponding automorphism(s).

%H A. Karttunen, <a href="/A089408/a089408.c.txt">C-program for computing the initial terms of this sequence</a>

%F a(0)=1, a(n) = A000108(n-1) if (n mod 3)=0 or 1 and a(n) = A000108(n-1)+A000108((n-2)/3) if (n mod 3)=2.

%p A089848 := n -> A000108(n-1)+`if`((2 = (n mod 3)), A000108((n-2)/3),0);

%o (Scheme) (define (A089848 n) (cond ((zero? n) 1) (else (+ (A000108 (- n 1)) (if (= 2 (modulo n 3)) (A000108 (/ (- n 2) 3)) 0)))))

%K nonn,easy

%O 0,3

%A _Antti Karttunen_, Nov 29 2003