A121781 Series expansion for mean-squared radius of gyration of Ferrers diagrams on square lattice.

0, 8, 66, 366, 1640, 6404, 22696, 74832, 233312, 695680, 2000128, 5578752, 15166464, 40336384, 105256960, 270135296, 683188224, 1705443328, 4207935488, 10274078720, 24848105472, 59579301888, 141734445056

Offset

1,2

Links

I. Jensen, Table of n, a(n) for n = 1..55 (from link below)

I. Jensen, Series expansions for self-avoiding polygons

Formula

Empirical (for n>=2): a(n) = 2^(n-7)*(50*n^3 + 3*n^2 + 70*n - 120 + 21*n^4)/3. - Vaclav Kotesovec, Nov 29 2012

Empirical G.f.: 5/16 - x/8 + (144*x^4 - 256*x^3 + 92*x^2 - 52*x + 5)/(16*(2*x-1)^5). - Vaclav Kotesovec, Nov 29 2012

Mathematica

Rest[CoefficientList[Series[5/16-x/8+(144*x^4-256*x^3+92*x^2-52*x+5)/(16*(2*x-1)^5), {x, 0, 20}], x]] (* Vaclav Kotesovec, Nov 29 2012 *)

Crossrefs

Sequence in context: A168302 A121782 A212784 * A121780 A121779 A051825

Adjacent sequences: A121778 A121779 A121780 * A121782 A121783 A121784

Keyword

nonn

Author

N. J. A. Sloane, Aug 30 2006

Status

approved