A121782 Series expansion for mean-squared radius of gyration of rectangles on square lattice.

0, 8, 66, 288, 900, 2280, 4998, 9856, 17928, 30600, 49610, 77088, 115596, 168168, 238350, 330240, 448528, 598536, 786258, 1018400, 1302420, 1646568, 2059926, 2552448, 3135000, 3819400, 4618458, 5546016, 6616988, 7847400

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

All terms appear to be generated by n^2*(n-1)*(n^2+2)/3. - T. D. Noe, Feb 09 2007

Conjectures from Colin Barker, Apr 17 2017: (Start)

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

a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.

(End)

Crossrefs

Sequence in context: A230736 A008893 A168302 * A212784 A121781 A121780

Adjacent sequences: A121779 A121780 A121781 * A121783 A121784 A121785

Keyword

nonn

Author

N. J. A. Sloane, Aug 30 2006

Status

approved