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%I #9 Apr 26 2021 10:18:03
%S 1,8,41,168,602,1968,6021,17512,48950,132496,349258,900368,2277556,
%T 5667936,13906221,33695208,80746846,191601872,450642654,1051472048,
%U 2435679852,5605044640,12820922530,29164511376,66004709148,148678206880
%N Number of Ferrers diagrams with a single Ferrers puncture with the same orientation inscribed strictly inside with half-perimeter = n.
%H Charles R Greathouse IV, <a href="/A133106/b133106.txt">Table of n, a(n) for n = 8..3296</a>
%F a(n) = [(2*n^2-16*n+6)*a(n-1)+(4*n^2-68*n+240)*a(n-2)-(8*n^2-88*n+240)*a(n-3)]/(n^2-14*n+48) with a(6)=0, a(7)=0, a(8)=1.
%F G.f.: (1-(1-4*x^2)^(1/2))*x^6/(2*(2*x-1)^4).
%e The sequence starts with n=8 because the smallest such object whose cartoon is below has a perimeter of 16. (1 denotes cell outside the puncture and 2 denotes cell inside the puncture).
%e 111
%e 121
%e 111
%Y Cf. A057410, A057406, A133107.
%K easy,nonn
%O 8,2
%A _Arvind Ayyer_, Sep 11 2007
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