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 A127302 Matula-Goebel signatures for plane binary trees encoded by A014486. 16
 1, 4, 14, 14, 86, 86, 49, 86, 86, 886, 886, 454, 886, 886, 301, 301, 301, 886, 886, 301, 454, 886, 886, 13766, 13766, 6418, 13766, 13766, 3986, 3986, 3986, 13766, 13766, 3986, 6418, 13766, 13766, 3101, 3101, 1589, 3101, 3101, 1849, 1849, 3101, 13766 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence maps A000108(n) oriented (plane) rooted binary trees encoded in range [A014137(n-1)..A014138(n-1)] of A014486 to A001190(n+1) non-oriented rooted binary trees, encoded by their Matula-Goebel numbers (when viewed as a subset of non-oriented rooted general trees). See also the comments at A127301. If the signature-permutation of a Catalan automorphism SP satisfies the condition A127302(SP(n)) = A127302(n) for all n, then it preserves the non-oriented form of a binary tree. Examples of such automorphisms include A069770, A057163, A122351, A069767/A069768, A073286-A073289, A089854, A089859/A089863, A089864, A122282, A123492-A123494, A123715/A123716, A127377-A127380, A127387 and A127388. A153835 divides natural numbers to same equivalence classes, i.e. a(i) = a(j) <=> A153835(i) = A153835(j) - Antti Karttunen, Jan 03 2013 LINKS FORMULA a(n) = A127301(A057123(n)). Can be also computed directly as a fold, see the Scheme-program. - Antti Karttunen, Jan 03 2013 EXAMPLE A001190(n+1) distinct values occur each range [A014137(n-1)..A014138(n-1)]. As an example, terms A014486(4..8) encode the following five plane binary trees: ........\/.....\/.................\/.....\/... .......\/.......\/.....\/.\/.....\/.......\/.. ......\/.......\/.......\_/.......\/.......\/. n=.....4........5........6........7........8.. The trees in positions 4, 5, 7 and 8 all produce Matula-Goebel number A000040(1)*A000040(A000040(1)*A000040(A000040(1)*A000040(1))) = 2*A000040(2*A000040(2*2)) = 2*A000040(14) = 2*43 = 86, as they are just different planar representations of the one and same non-oriented tree. The tree in position 6 produces Matula-Goebel number A000040(A000040(1)*A000040(1)) * A000040(A000040(1)*A000040(1)) = A000040(2*2) * A000040(2*2) = 7*7 = 49. Thus a(4..8) = 86,86,49,86,86. PROG (Scheme with Antti Karttunen's IntSeq-library, definition added here Jan 03 2013): (definec (A127302 n) (*A127302 (A014486->parenthesization (A014486 n)))) (define (*A127302 s) (fold-right (lambda (t m) (* (A000040 (*A127302 t)) (A000040 m))) 1 s)) CROSSREFS Cf A127301, A153835, A153829. Sequence in context: A200553 A229392 A229320 * A204541 A020157 A101237 Adjacent sequences:  A127299 A127300 A127301 * A127303 A127304 A127305 KEYWORD nonn AUTHOR Antti Karttunen, Jan 16 2007 STATUS approved

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Last modified July 5 06:18 EDT 2022. Contains 355088 sequences. (Running on oeis4.)