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%I #24 Aug 14 2021 11:39:31
%S 1,15,50,225,590,1485,3130,6435,11931,21450,36220,59670,94140,145350,
%T 217500,319770,458981,648945,900350,1233375,1663850,2220075,2924870,
%U 3817125,4928511,6310980,8007640,10086780,12605560,15651900,19300440,23662980,28835081
%N Number of symmetric types of (4,2n)-hypergraphs under action of complementing group C(4,2).
%C The first g.f. gives a 0 between each two terms of the sequence - _Colin Barker_, Jul 12 2013
%H Vincenzo Librandi, <a href="/A029941/b029941.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,-4,11,-8,0,8,-10,0,8,0,-10,8,0,-8,11,-4,-4,4,-1).
%F G.f.: (30/(1-x^2)^8-70/(1-x^4)^4+120/(1-x^8)^2-64/(1-x^16))/16.
%F G.f.: (9*x^12 -21*x^11 +26*x^10 +121*x^9 -149*x^8 +132*x^7 +20*x^6 +68*x^5 -61*x^4 +89*x^3 -6*x^2 +11*x +1) / ((x-1)^8 *(x+1)^4 *(x^2+1)^2 *(x^4+1)). - _Colin Barker_, Jul 12 2013
%F a(n) = 4*a(n-1)-4*a(n-2)-4*a(n-3)+11*a(n-4)-8*a(n-5)+8*a(n-7)-10*a(n-8)+8*a(n-10)-10*a(n-12)+8*a(n-13)-8*a(n-15)+11*a(n-16)-4*a(n-17)-4*a(n-18)+4*a(n-19)-a(n-20). - _Wesley Ivan Hurt_, May 24 2021
%t CoefficientList[Series[(9 x^12 - 21 x^11 + 26 x^10 + 121 x^9 - 149 x^8 + 132 x^7 + 20 x^6 + 68 x^5 - 61 x^4 + 89 x^3 - 6 x^2 + 11 x + 1)/((x - 1)^8 (x + 1)^4 (x^2 + 1)^2 (x^4 + 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 19 2013 *)
%t LinearRecurrence[{4,-4,-4,11,-8,0,8,-10,0,8,0,-10,8,0,-8,11,-4,-4,4,-1},{1,15,50,225,590,1485,3130,6435,11931,21450,36220,59670,94140,145350,217500,319770,458981,648945,900350,1233375},40] (* _Harvey P. Dale_, Aug 14 2021 *)
%Y Cf. A051502.
%K nonn,easy
%O 0,2
%A _Vladeta Jovovic_, Jul 13 2000
%E More terms from _James A. Sellers_, Aug 08 2000
%E More terms from _Colin Barker_, Jul 12 2013
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