A089407 Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A089859/A089863.

1, 1, 1, 2, 4, 11, 34, 109, 360, 1219, 4206, 14708, 52024, 185758, 668676, 2423821, 8839632, 32411555, 119410390, 441817020, 1641032536, 6116570954, 22870649308, 85764918130, 322476066224, 1215486652366, 4591838372044, 17383387914792

Offset: 0

Author

Antti Karttunen, Nov 29 2003

Keywords

• nonn
• easy

Comments

The number of orbits to which the corresponding automorphism(s) partitions the set of A000108(n) binary trees with n internal nodes.

Links

• A. Karttunen, C-program for computing the initial terms of this sequence

Programs

Scheme

(define (A089407 n) (if (< n 2) 1 (* (/ 1 4) (+ (A000108 n) (A089408 n) (if (= 3 (modulo n 4)) (* 2 (A000108 (/ (- n 3) 4))) 0)))))

Formula

a(0) = a(1) = 1, a(n) = (1/4)*(A000108(n) + A089408(n) + (if (n == 3 mod 4) 2*A000108((n-3)/4)))