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A057547
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A014486-encodings of Catalan mountain ranges with no sea-level valleys, i.e. the rooted plane general trees with root degree = 1.
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4
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2, 12, 52, 56, 212, 216, 228, 232, 240, 852, 856, 868, 872, 880, 916, 920, 932, 936, 944, 964, 968, 976, 992, 3412, 3416, 3428, 3432, 3440, 3476, 3480, 3492, 3496, 3504, 3524, 3528, 3536, 3552, 3668, 3672, 3684, 3688, 3696, 3732, 3736, 3748, 3752, 3760
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| This one-to-one correspondence between all rooted plane trees and one node larger, root degree = 1 trees illustrates the fact that INVERT(A000108) = LEFT(A000108). (Catalan numbers shift left under Cameron's A transformation.)
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REFERENCES
| P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102; also in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.
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LINKS
| Index entries for encodings of plane rooted trees
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FORMULA
| a(n) = A014486(A057548(n)) and also from n>0 onward = A079946(A014486(n))
a(n) = alltrees2singletrunked(A014486[n]) (see Maple code below and in A057501).
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MAPLE
| alltrees2singletrunked := n -> pars2binexp([binexp2pars(n)]); # Just surround with extra parentheses.
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CROSSREFS
| Double-trunked trees: A057517. Cf. also A057548, A057549.
Sequence in context: A198008 A054667 A009537 * A043007 A176580 A179259
Adjacent sequences: A057544 A057545 A057546 * A057548 A057549 A057550
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (HisFirstname.HisSurname(AT)iki.fi) Sep 07 2000
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