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 A057547 A014486-encodings of Catalan mountain ranges with no sea-level valleys, i.e., the rooted plane general trees with root degree = 1. 5

%I

%S 2,12,52,56,212,216,228,232,240,852,856,868,872,880,916,920,932,936,

%T 944,964,968,976,992,3412,3416,3428,3432,3440,3476,3480,3492,3496,

%U 3504,3524,3528,3536,3552,3668,3672,3684,3688,3696,3732,3736,3748,3752,3760

%N A014486-encodings of Catalan mountain ranges with no sea-level valleys, i.e., the rooted plane general trees with root degree = 1.

%C 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.)

%D 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.

%H <a href="/index/Ro#RootedTreePlanEncodings">Index entries for encodings of plane rooted trees</a>

%F a(n) = A014486(A057548(n)) and also from n > 0 onward = A079946(A014486(n)).

%F a(n) = alltrees2singletrunked(A014486[n]) (see Maple code below and in A057501).

%p alltrees2singletrunked := n -> pars2binexp([binexp2pars(n)]); # Just surround with extra parentheses.

%Y Double-trunked trees: A057517. Cf. also A057548, A057549.

%K nonn

%O 0,1

%A _Antti Karttunen_ Sep 07 2000

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