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A055780
Number of symmetric types of (3,2n)-hypergraphs under action of complementing group C(3,2).
1
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
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
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