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 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 Indranil Ghosh, Table of n, a(n) for n = 0..1000 Antti Karttunen, C-program for computing the initial terms of this sequence 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 Adjacent sequences: A089405 A089406 A089407 * A089409 A089410 A089411 KEYWORD nonn,easy AUTHOR Antti Karttunen, Nov 29 2003 STATUS approved

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