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%I #42 Mar 11 2023 13:07:18
%S 1,6,22,64,162,372,792,1584,3003,5434,9438,15808,25636,40392,62016,
%T 93024,136629,196878,278806,388608,533830,723580,968760,1282320,
%U 1679535,2178306,2799486,3567232,4509384
%N T(2n+4,n), array T as in A055794.
%C If Y is a 2-subset of an n-set X then, for n>=7, a(n-7) is the number of 7-subsets of X which do not have exactly one element in common with Y. - _Milan Janjic_, Dec 28 2007
%H Vincenzo Librandi, <a href="/A055797/b055797.txt">Table of n, a(n) for n = 0..1000</a>
%H Alexsandar Petojevic, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL5/Petojevic/petojevic5.html">The Function vM_m(s; a; z) and Some Well-Known Sequences</a>, Journal of Integer Sequences, Vol. 5 (2002), Article 02.1.7
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).
%F a(n-5) = binomial(n,7) + binomial(n,5) for n>4. - _Zerinvary Lajos_, Jul 24 2006
%F G.f.: (1-2*x+2*x^2)/(1-x)^8. - _Colin Barker_, Feb 22 2012
%F a(n) = 8*(n-1) - 28*(n-2) + 56*(n-3) - 70*(n-4) + 56*(n-5) - 28*(n-6) + 8*(n-7) - (n-8). - _Vincenzo Librandi_, May 01 2012
%F a(n) = (n+5)*(n+4)*(n+3)*(n+2)*(n+1)*(n^2-n+42)/5040. - _R. J. Mathar_, Oct 01 2021
%p [seq(binomial(n,7)+binomial(n,5), n=5..34)]; # _Zerinvary Lajos_, Jul 24 2006
%t a=1;b=2;c=3;d=4;e=5;f=6;s=7;lst={s};Do[a+=n;b+=a;c+=b;d+=c;e+=d;f+=e;s+=f;AppendTo[lst,s],{n,6!}];lst (* _Vladimir Joseph Stephan Orlovsky_, May 24 2009 *)
%t CoefficientList[Series[(1-2*x+2*x^2)/(1-x)^8,{x,0,30}],x] (* _Vincenzo Librandi_, May 01 2012 *)
%t LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,6,22,64,162,372,792,1584},30] (* _Harvey P. Dale_, Mar 11 2023 *)
%o (Magma) [Binomial(n,7) + Binomial(n,5): n in [5..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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