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A079438
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Number of rooted general plane trees which are symmetric and will stay symmetric also after the underlying plane binary tree has been reflected, i.e. number of integers i in range [A014137(n-1)..A014138(n-1)] such that A057164(i)=i and A057164(A057163(i)) = A057163(i).
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7
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1, 1, 2, 2, 2, 4, 4, 4, 6, 6, 6, 8, 8, 8, 12, 12, 12, 14, 16, 16, 18, 18, 22, 24, 24, 24, 28, 28, 28, 30, 34, 34, 36, 36, 38, 40, 40, 40, 46, 46, 46, 48, 50, 50, 52, 52, 56, 58, 58, 58, 62, 62, 62, 64, 68, 68, 70, 70, 72, 74, 74, 74, 80, 80, 80, 82, 84, 84, 86, 86, 90, 92, 92, 92
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| Also number of fixed points in range [A014137(n-1)..A014138(n-1)] of permutation A071661 (= Donaghey's automorphism M "squared"), which is equal to condition A057164(i)=A069787(i)=i, i.e. the size of the intersect of fixed points of permutations A057164 and A069787 in the same range.
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REFERENCES
| R. Donaghey, Automorphisms on Catalan trees and bracketing, J. Combin. Theory, Series B, 29 (1980), 75-90.
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LINKS
| A. Karttunen, C-program for counting the initial terms of this sequence (empirically)
A. Karttunen, Illustration of initial terms for trees of sizes n=2..18
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FORMULA
| a(0)=a(1)=1, a(n) = 2*(floor((n+1)/3) + (if n>=14) (floor((n-10)/4)+floor((n-14)/8))) [This is the correct formula if the conjecture given in A080070 is true, otherwise it is only a lower bound, although known to be exact for up to very high values of n.]
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MAPLE
| A079438 := n -> `if`((n<2), 1, 2*(floor((n+1)/3) + `if`((n>=14), floor((n-10)/4)+floor((n-14)/8), 0)));
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CROSSREFS
| From n>= 2 onward A079440(n) = a(n)/2.
Occurs in A073202 as row 13373289. Cf. A079437, A079439, A079442, A080070.
Sequence in context: A054861 A187324 A086227 * A123050 A113694 A086159
Adjacent sequences: A079435 A079436 A079437 * A079439 A079440 A079441
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (Firstname.Surname(AT)iki.fi) Jan 27 2003
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