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A121703 Number of alternating separable permutations. 1
1, 2, 4, 8, 20, 48, 132, 344, 996, 2720, 8132, 22888, 69941, 201029, 624077, 1821359, 5722885, 16919312, 53779406, 159276786 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

Table of n, a(n) for n=1..20.

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. A121704.

Sequence in context: A288476 A056952 A225585 * A301467 A275070 A115219

Adjacent sequences:  A121700 A121701 A121702 * A121704 A121705 A121706

KEYWORD

nonn

AUTHOR

Vincent Vatter, Aug 16 2006

STATUS

approved

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Last modified February 25 20:04 EST 2020. Contains 332258 sequences. (Running on oeis4.)