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A133106 Number of Ferrers diagrams with a single Ferrers puncture with the same orientation inscribed strictly inside with half-perimeter = n.

%I A133106 #11 Sep 21 2024 16:51:58
%S A133106 1,8,41,168,602,1968,6021,17512,48950,132496,349258,900368,2277556,
%T A133106 5667936,13906221,33695208,80746846,191601872,450642654,1051472048,
%U A133106 2435679852,5605044640,12820922530,29164511376,66004709148,148678206880
%N A133106 Number of Ferrers diagrams with a single Ferrers puncture with the same orientation inscribed strictly inside with half-perimeter = n.
%H A133106 Charles R Greathouse IV, <a href="/A133106/b133106.txt">Table of n, a(n) for n = 8..3296</a>
%F A133106 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 A133106 G.f.: (1-(1-4*x^2)^(1/2))*x^6/(2*(2*x-1)^4).
%e A133106 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 A133106 111
%e A133106 121
%e A133106 111
%t A133106 Drop[CoefficientList[Series[(1-(1-4x^2)^(1/2))x^6/(2(2x-1)^4),{x,0,40}],x],8] (* _Harvey P. Dale_, Sep 21 2024 *)
%Y A133106 Cf. A057410, A057406, A133107.
%K A133106 easy,nonn
%O A133106 8,2
%A A133106 _Arvind Ayyer_, Sep 11 2007