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%I #29 Sep 08 2022 08:45:01
%S 1,8,37,130,385,1012,2431,5434,11440,22880,43758,80444,142766,245480,
%T 410210,667964,1062347,1653608,2523675,3782350,5574855,8090940,
%U 11575785,16342950,22789650,31414656,42839148,57830872
%N T(2n+6,n), array T as in A055794.
%C If Y is a 2-subset of an n-set X then, for n>=9, a(n-9) is the number of 9-subsets of X which do not have exactly one element in common with Y. - _Milan Janjic_, Dec 28 2007
%H Vincenzo Librandi, <a href="/A055799/b055799.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
%F a(n-9) = binomial(n,9) - 2*binomial(n-2,8), n=9, 10, ... . - _Milan Janjic_, Dec 28 2007
%F G.f.: (1-2*x+2*x^2)/(1-x)^10. - _Colin Barker_, Feb 21 2012
%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4)+ 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10). - _Vincenzo Librandi_, May 01 2012
%t a=1;b=2;c=3;d=4;e=5;f=6;g=7;s=8;lst={1,s};Do[a+=n;b+=a;c+=b;d+=c;e+=d;f+=e;g+=f;s+=g;AppendTo[lst,s],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, May 24 2009 *)
%t CoefficientList[Series[(1-2*x+2*x^2)/(1-x)^10,{x,0,30}],x] (* _Vincenzo Librandi_, May 01 2012 *)
%o (Magma) [Binomial(n,9)-2*Binomial(n-2,8):n in [9..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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