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A057517 Binary encodings of the Catalan mountain ranges with exactly one sea-level valley, i.e., the rooted plane trees with root degree = 2. 6

%I #5 Aug 03 2017 00:41:22

%S 10,44,50,180,184,204,210,226,724,728,740,744,752,820,824,844,850,866,

%T 908,914,930,962,2900,2904,2916,2920,2928,2964,2968,2980,2984,2992,

%U 3012,3016,3024,3040,3284,3288,3300,3304,3312,3380,3384,3404,3410,3426

%N Binary encodings of the Catalan mountain ranges with exactly one sea-level valley, i.e., the rooted plane trees with root degree = 2.

%C This bijective mapping from all rooted plane trees to one node larger, root degree = 2 trees illustrates the fact that CONV(A000108, A000108) = LEFT(A000108). (Catalan numbers shift left under convolution).

%F a(n) = alltrees2doubletrunked(A014486(n)) (Starting from n=1).

%p alltrees2doubletrunked := n -> pars2binexp(alltrees2doubletrunkedP(binexp2pars(n)));

%p alltrees2doubletrunkedP := h -> [car(h),cdr(h)];

%Y Cf. A057501 (for binexp2pars, pars2binexp, car, cdr), A057518, A057519, A057122. Single-trunked trees: A057547.

%K nonn

%O 1,1

%A _Antti Karttunen_, Sep 03 2000

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