id:A121703 - OEIS Search Results

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Number of alternating separable permutations.

+0
2

1, 2, 4, 8, 20, 48, 132, 344, 996, 2720, 8132, 22888, 69941, 201029, 624077, 1821359, 5722885, 16919312, 53779406, 159276786 (list; graph; listen)

	OFFSET	`1,2`
	COMMENT	`The separable permutations are those avoiding 2413 and 3142 and are counted by the large Schroeder numbers (A006318). The alternating permutations are counted by the Euler numbers (A000111).`
	LINKS	`R. Brignall, S. Huczynska and V. Vatter, Simple permutations and algebraic generating functions, arXiv:math.CO/0608391.`
	FORMULA	`G.f. satisfies f^3-(2x^2-5x+4)f^2-(4x^3+x^2-8x)f-(2x^4+5x^3+4x^2)=0.`
	EXAMPLE	`a(4)=8 because of the 10 alternating permutations of length 4, 2413 and 3142 are not separable.`
	CROSSREFS	`Cf. C.f. A121704.` `Adjacent sequences: A121700 A121701 A121702 this_sequence A121704 A121705 A121706` `Sequence in context: A051389 A078006 A056952 this_sequence A115219 A078160 A089976`
	KEYWORD	`nonn`
	AUTHOR	`Vince Vatter (vince(AT)mcs.st-and.ac.uk), Aug 16 2006`

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Last modified October 7 14:39 EDT 2008. Contains 144666 sequences.