A055780 Number of symmetric types of (3,2n)-hypergraphs under action of complementing group C(3,2).

1, 7, 14, 35, 57, 98, 140, 210, 281, 385, 490, 637, 785, 980, 1176, 1428, 1681, 1995, 2310, 2695, 3081, 3542, 4004, 4550, 5097, 5733, 6370, 7105, 7841, 8680, 9520, 10472, 11425, 12495, 13566, 14763, 15961, 17290, 18620, 20090, 21561, 23177, 24794, 26565

Offset

0,2

Comments

The first g.f. gives a 0 between each two terms of the sequence - Colin Barker, Jul 12 2013

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (2,0,-2,2,-2,0,2,-1).

Formula

G.f.: -(x^8-9*x^6-5*x^2-1)/(1-x^2)^2/(1-x^4)/(1-x^8).

G.f.: -(x^4-9*x^3-5*x-1) / ((x-1)^4*(x+1)^2*(x^2+1)). - Colin Barker, Jul 12 2013

Example

There are 7 symmetric (3,2)-hypergraphs under action of complementing group C(3,2): {{1,2},{1,2,3}}, {{1,3},{1,2,3}}, {{1,2},{1,3}}, {{2,3},{1,2,3}}, {{1,2},{2,3}}, {{1,3},{2,3}}, {{1},{2,3}}.

Maple

gf := -(x^8-9*x^6-5*x^2-1)/(1-x^2)^2/(1-x^4)/(1-x^8): s := series(gf, x, 200): for i from 0 to 200 by 2 do printf(`%d, `, coeff(s, x, i)) od:

Mathematica

LinearRecurrence[{2, 0, -2, 2, -2, 0, 2, -1}, {1, 7, 14, 35, 57, 98, 140, 210}, 50] (* Harvey P. Dale, May 15 2020 *)

Crossrefs

Sequence in context: A134384 A352851 A304143 * A161814 A333594 A067048

Adjacent sequences: A055777 A055778 A055779 * A055781 A055782 A055783

Keyword

nonn,easy

Author

Vladeta Jovovic, Jul 13 2000

Extensions

More terms from James A. Sellers, Jul 13 2000

More terms from Colin Barker, Jul 12 2013

Status

approved