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

8,2

Links

Charles R Greathouse IV, Table of n, a(n) for n = 8..3296

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).

Example

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

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 *)

Crossrefs

Cf. A057410, A057406, A133107.

Sequence in context: A171714 A342034 A304160 * A358588 A272843 A268997

Adjacent sequences: A133103 A133104 A133105 * A133107 A133108 A133109

Keyword

easy,nonn

Author

Arvind Ayyer, Sep 11 2007

Status

approved