A057514 - OEIS

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A057514

Number of peaks in mountain ranges encoded by A014486, number of leaves in the corresponding rooted plane trees. (the root node is never counted as a leaf).

0, 1, 2, 1, 3, 2, 2, 2, 1, 4, 3, 3, 3, 2, 3, 2, 3, 3, 2, 2, 2, 2, 1, 5, 4, 4, 4, 3, 4, 3, 4, 4, 3, 3, 3, 3, 2, 4, 3, 3, 3, 2, 4, 3, 4, 4, 3, 3, 3, 3, 2, 3, 2, 3, 3, 2, 3, 3, 3, 2, 2, 2, 2, 2, 1, 6, 5, 5, 5, 4, 5, 4, 5, 5, 4, 4, 4, 4, 3, 5, 4, 4, 4, 3, 5, 4, 5, 5, 4, 4, 4, 4, 3, 4, 3, 4, 4, 3, 4, 4, 4, 3, 3, 3, 3 (list; graph; refs; listen; history; internal format)

	OFFSET	`0,3`
	COMMENTS	`Partial sums from A014137[i]th to A014137[i+1]-1:th term of this sequence produce central binomial coefficients C(2n+1,n+1) (see comment at A001700): [seq(add(A057514[j],j=CatPsum(i)..(CatPsum(i+1)-1)),i=0..upto_n)];`
	LINKS	`A. Karttunen, Gatomorphisms and other excursions ... (Includes Scheme program)`
	FORMULA	`a(n) = wt(GrayCode(A014486[n]))/2 = A000120[A003188[A014486[n]]]/2 = A005811[A014486[n]]/2`
	MAPLE	`Cat := n -> binomial(2*n, n)/(n+1); CatPsum := proc(n) option remember; if(0 = n) then RETURN(1); else RETURN(Cat(n)+CatPsum(n-1)); fi; end;`
	CROSSREFS	`Cf. A057515. For Maple procedure GrayCode see A055095. a(n)-1 gives the number of zeros in A071153(n) (for n>=1).` `Sequence in context: A071481 A162348 A084216 * A140720 A033559 A103151` `Adjacent sequences: A057511 A057512 A057513 * A057515 A057516 A057517`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen Sep 03 2000`

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Last modified February 15 09:15 EST 2012. Contains 205753 sequences.