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%I #19 Mar 18 2024 16:47:00
%S 1,7,14,35,57,98,140,210,281,385,490,637,785,980,1176,1428,1681,1995,
%T 2310,2695,3081,3542,4004,4550,5097,5733,6370,7105,7841,8680,9520,
%U 10472,11425,12495,13566,14763,15961,17290,18620,20090,21561,23177,24794,26565
%N Number of symmetric types of (3,2n)-hypergraphs under action of complementing group C(3,2).
%C The first g.f. gives a 0 between each two terms of the sequence - _Colin Barker_, Jul 12 2013
%H Harvey P. Dale, <a href="/A055780/b055780.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,-2,2,-2,0,2,-1).
%F G.f.: -(x^8-9*x^6-5*x^2-1)/(1-x^2)^2/(1-x^4)/(1-x^8).
%F G.f.: -(x^4-9*x^3-5*x-1) / ((x-1)^4*(x+1)^2*(x^2+1)). - _Colin Barker_, Jul 12 2013
%e 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}}.
%p 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:
%t LinearRecurrence[{2,0,-2,2,-2,0,2,-1},{1,7,14,35,57,98,140,210},50] (* _Harvey P. Dale_, May 15 2020 *)
%K nonn,easy
%O 0,2
%A _Vladeta Jovovic_, Jul 13 2000
%E More terms from _James A. Sellers_, Jul 13 2000
%E More terms from _Colin Barker_, Jul 12 2013
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