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%I #34 Sep 08 2022 08:45:01
%S 1,7,29,93,255,627,1419,3003,6006,11440,20878,36686,62322,102714,
%T 164730,257754,394383,591261,870067,1258675,1792505,2516085,3484845,
%U 4767165,6446700,8625006,11424492,14991724,19501108,25158980,32208132,40932804,51664173
%N T(2n+5,n), array T as in A055794.
%C If Y is a 2-subset of an n-set X then, for n>=8, a(n-8) is the number of 8-subsets of X which do not have exactly one element in common with Y. - _Milan Janjic_, Dec 28 2007
%H Vincenzo Librandi, <a href="/A055798/b055798.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (9,-36,84,-126,126,-84,36,-9,1).
%F a(n-8) = binomial(n,8)-2*binomial(n-2,7), n=8,9,10,.... - _Milan Janjic_, Dec 28 2007
%F G.f.: (1-2*x+2*x^2)/(1-x)^9. [_Colin Barker_, Feb 22 2012]
%F a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9). - _Vincenzo Librandi_, May 01 2012
%t CoefficientList[Series[(-2*(z - 1)*z - 1)/(z - 1)^9, {z, 0, 100}], z] (* _Vladimir Joseph Stephan Orlovsky_, Jul 16 2011 *)
%t LinearRecurrence[{9,-36,84,-126,126,-84,36,-9,1},{1,7,29,93,255,627,1419,3003,6006},50] (* _Vincenzo Librandi_, May 01 2012 *)
%o (Magma) [Binomial(n,8)-2*Binomial(n-2,7): n in [8..40]]; // _Vincenzo Librandi_, May 01 2012
%Y Cf. A051601.
%K nonn,easy
%O 0,2
%A _Clark Kimberling_, May 28 2000
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