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A121703 Number of alternating separable permutations. 1


%S 1,2,4,8,20,48,132,344,996,2720,8132,22888,69941,201029,624077,

%T 1821359,5722885,16919312,53779406,159276786

%N Number of alternating separable permutations.

%C 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).

%H R. Brignall, S. Huczynska and V. Vatter, <a href="http://arXiv.org/abs/math.CO/0608391">Simple permutations and algebraic generating functions</a>, arXiv:math.CO/0608391.

%F G.f. satisfies f^3-(2x^2-5x+4)f^2-(4x^3+x^2-8x)f-(2x^4+5x^3+4x^2)=0.

%e a(4)=8 because of the 10 alternating permutations of length 4, 2413 and 3142 are not separable.

%Y Cf. A121704.

%K nonn

%O 1,2

%A _Vincent Vatter_, Aug 16 2006

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Last modified June 24 14:24 EDT 2021. Contains 345417 sequences. (Running on oeis4.)