A133106 Number of Ferrers diagrams with a single Ferrers puncture with the same orientation inscribed strictly inside with half-perimeter = n.
1, 8, 41, 168, 602, 1968, 6021, 17512, 48950, 132496, 349258, 900368, 2277556, 5667936, 13906221, 33695208, 80746846, 191601872, 450642654, 1051472048, 2435679852, 5605044640, 12820922530, 29164511376, 66004709148, 148678206880
Offset: 8
Examples
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). 111 121 111
Links
- Charles R Greathouse IV, Table of n, a(n) for n = 8..3296
Programs
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Mathematica
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 *)
Formula
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.
G.f.: (1-(1-4*x^2)^(1/2))*x^6/(2*(2*x-1)^4).