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Search: id:A057517
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| A057517 |
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Binary encodings of the Catalan mountain ranges with exactly one sea-level valley, i.e. the rooted plane trees with root degree = 2. |
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+0
7
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| 10, 44, 50, 180, 184, 204, 210, 226, 724, 728, 740, 744, 752, 820, 824, 844, 850, 866, 908, 914, 930, 962, 2900, 2904, 2916, 2920, 2928, 2964, 2968, 2980, 2984, 2992, 3012, 3016, 3024, 3040, 3284, 3288, 3300, 3304, 3312, 3380, 3384, 3404, 3410, 3426
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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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).
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FORMULA
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a(n) = alltrees2doubletrunked(A014486[n]) [Starting from n=1].
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MAPLE
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alltrees2doubletrunked := n -> pars2binexp(alltrees2doubletrunkedP(binexp2pars(n)));
alltrees2doubletrunkedP := h -> [car(h), cdr(h)];
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CROSSREFS
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Cf. A057501 (for binexp2pars, pars2binexp, car, cdr), A057518, A057519, A057122. Single-trunked trees: A057547.
Sequence in context: A084036 A092117 A003866 this_sequence A126964 A008532 A085582
Adjacent sequences: A057514 A057515 A057516 this_sequence A057518 A057519 A057520
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen Sep 03 2000
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