A113920 G.f.: (x^3 - x + 1)^3/(x^3*(1 - x)^3).

1, 0, 0, 3, 3, 3, 6, 9, 12, 16, 21, 27, 34, 42, 51, 61, 72, 84, 97, 111, 126, 142, 159, 177, 196, 216, 237, 259, 282, 306, 331, 357, 384, 412, 441, 471, 502, 534, 567, 601, 636, 672, 709, 747, 786, 826, 867, 909, 952, 996, 1041, 1087, 1134, 1182, 1231, 1281, 1332, 1384, 1437

Offset

-3,4

Comments

Series expansion of elliptical invariant for a cubic anharmonic group. Suggested by the anharmonic group elliptical invariant A078907.

If Y is a 4-subset of an n-set X then, for n>=7, a(n-3) is the number of 2-subsets of X which do not have exactly one element in common with Y. - Milan Janjic, Dec 28 2007

References

McKean and Moll, Elliptic Curves, 1997, Cambridge University Press, page 20.

Links

Table of n, a(n) for n=-3..55.

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n-7)=1/2*n^2-9/2*n+16, n=7,8,9,... - Milan Janjic, Dec 28 2007

Mathematica

b = ReplacePart[Table[Coefficient[Series[(x^3 - x + 1)^3/(x^3*(1 - x)^3), {x, 0, 30}], x^n], {n, -3, 30}], 3, 4]

Crossrefs

Cf. A078907.

Sequence in context: A348224 A141094 A132972 * A081848 A079988 A212091

Adjacent sequences: A113917 A113918 A113919 * A113921 A113922 A113923

Keyword

nonn,easy

Author

Roger L. Bagula, Jan 29 2006

Extensions

Edited by N. J. A. Sloane, Apr 21 2007

Status

approved