The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A089408 Number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A089864. 90
1, 1, 2, 1, 2, 2, 4, 5, 10, 14, 28, 42, 84, 132, 264, 429, 858, 1430, 2860, 4862, 9724, 16796, 33592, 58786, 117572, 208012, 416024, 742900, 1485800, 2674440, 5348880, 9694845, 19389690, 35357670, 70715340, 129644790, 259289580, 477638700 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
The number of n-node binary trees fixed by the corresponding automorphism(s). Essentially A000108 interleaved with A068875.
LINKS
FORMULA
a(0)=1, a(2n) = 2*A000108(n-1), a(2n+1) = A000108(n)
G.f.: (1+4x-(1+2x)sqrt(1-4x^2))/(2x). - Paul Barry, Apr 11 2005
C(2*j,j)/(1+j)*i, i=1..2), j >= 0. - Zerinvary Lajos, Apr 29 2007
D-finite with recurrence: (n+1)*a(n) - 2*a(n-1) + 4(3-n)*a(n-2) = 0. - R. J. Mathar, Dec 17 2011, corrected by Georg Fischer, Feb 13 2020
MAPLE
seq(seq(binomial(2*j, j)/(1+j)*i, i=1..2), j=0..19); # Zerinvary Lajos, Apr 29 2007
MATHEMATICA
a[0] = 1; a[n_] := If[EvenQ[n], 2*CatalanNumber[n/2 - 1], CatalanNumber[(n-1)/2]]; Table[a[n], {n, 0, 40}] (* Jean-François Alcover, Jul 24 2013 *)
PROG
(Scheme) (define (A089408 n) (cond ((zero? n) 1) ((even? n) (* 2 (A000108 (-1+ (/ n 2))))) (else (A000108 (/ (-1+ n) 2)))))
(Python)
from sympy import catalan
def a(n): return 1 if n==0 else 2*catalan(n//2 - 1) if n%2==0 else catalan((n - 1)//2) # Indranil Ghosh, May 23 2017
CROSSREFS
Cf. A089402.
Cf. A000108.
Sequence in context: A225044 A325246 A193691 * A350287 A208888 A258783
KEYWORD
nonn,easy
AUTHOR
Antti Karttunen, Nov 29 2003
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 18 11:36 EDT 2024. Contains 372630 sequences. (Running on oeis4.)