id:A130918 - OEIS Search Results

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Simple self-inverse permutation of natural numbers: List each block of A000108(n) numbers from A014137(n-1) to A014138(n-1) in reverse order.

+0
2

0, 1, 3, 2, 8, 7, 6, 5, 4, 22, 21, 20, 19, 18, 17, 16, 15, 14, 13, 12, 11, 10, 9, 64, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 196, 195, 194, 193, 192 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`In principle this involution is the signature permutation of yet another Catalan automorphism. However, the question remains what is the most "natural" way to create such an automorphism acting e.g. on S-expressions (i.e. rooted plane binary trees), which would produce this sequence as its signature permutation.`
	LINKS	`A. Karttunen, Table of n, a(n) for n = 0..2055` `Index entries for signature-permutations of Catalan automorphisms`
	FORMULA	`a(0)=0, a(n) = A014138(A072643(n)-1) - A082853(n).`
	PROGRAM	`(Scheme:) (define (A130918 n) (if (zero? n) n (- (A014138 (- (A072643 n) 1)) (A082853 n))))`
	CROSSREFS	`Inverse: A130918. Cf. A054429, A057163. The number of cycles and the number of fixed points in range [A014137(n-1)..A014138(n-1)] of this permutation are given by A130380 and A036987.` `Sequence in context: A082348 A122339 A057163 this_sequence A021308 A060921 A095013` `Adjacent sequences: A130915 A130916 A130917 this_sequence A130919 A130920 A130921`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jun 11 2007`

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Last modified November 30 22:12 EST 2008. Contains 150989 sequences.

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