A133107 Number of Ferrers diagrams with a single strictly smaller Ferrers puncture with the same orientation removed from the top with half-perimeter = n.

1, 7, 32, 121, 410, 1294, 3888, 11273, 31826, 88041, 239734, 644758, 1717191, 4538129, 11919760, 31156313, 81125827, 210604604, 545462798, 1410226551, 3641097828, 9391872711, 24208902420, 62373915102, 160663604377

Offset

6,2

Links

Arvind Ayyer, Sep 11 2007, Table of n, a(n) for n = 6..76

Formula

G.f.: x^2*(-1 + 3*x - x^2 + (5*x^4 - 6*x^3 + 11*x^2 - 6*x + 1 + 4*x^6 - 12*x^5)^(1/2))/(2*(x^2 - 3*x + 1)*(1-2*x)^2)

Example

The sequence starts with n=6 because the smallest such object whose illustration is below has a perimeter of 12. (1 denotes cell inside the Ferrers diagram.)
1 1
111

Crossrefs

Cf. A057410, A057406, A133106.

Sequence in context: A182820 A001794 A140289 * A178851 A213163 A249999

Adjacent sequences: A133104 A133105 A133106 * A133108 A133109 A133110

Keyword

easy,nonn

Author

Arvind Ayyer, Sep 11 2007

Status

approved