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%I #21 Jan 30 2020 21:29:18
%S 1,1,1,2,5,12,29,72,182,466,1207,3158,8334,22158,59299,159614,431838,
%T 1173710,3203244,8774780,24118522,66497316,183858411,509670494,
%U 1416231616,3944027402,11006186760,30772507128,86191006746,241815195292
%N Number of valid hook configurations of permutations of [n] that avoid the patterns 231 and 321.
%C Essentially the same as A217333 and A025273. - _R. J. Mathar_, May 17 2019
%H Colin Defant, <a href="http://arxiv.org/abs/1904.10451">Motzkin intervals and valid hook configurations</a>, arXiv preprint arXiv:1904.10451 [math.CO], 2019.
%F G.f.: (1 - 2*x + 2*x^2 - sqrt(1 - 4*x + 4*x^2 - 4*x^3 + 4*x^4)) / (2*x^2).
%F D-finite with recurrence: (n+2)*a(n) +2*(-2*n-1)*a(n-1) +4*(n-1)*a(n-2) +2*(-2*n+5)*a(n-3) +4*(n-4)*a(n-4)=0. - _R. J. Mathar_, May 17 2019
%o (PARI) my(x='x+O('x^35)); Vec((1 - 2*x + 2*x^2 - sqrt(1 - 4*x + 4*x^2 - 4*x^3 + 4*x^4))/(2*x^2)) \\ _Michel Marcus_, May 08 2019
%Y Cf. A307786, A307787.
%K nonn
%O 0,4
%A _Colin Defant_, Apr 28 2019
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