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%I #27 Sep 08 2022 08:45:01
%S 1,15,32,56,88,129,180,242,316,403,504,620,752,901,1068,1254,1460,
%T 1687,1936,2208,2504,2825,3172,3546,3948,4379,4840,5332,5856,6413,
%U 7004,7630,8292,8991,9728,10504,11320,12177,13076
%N a(n) = T(n,n-4), array T as in A055807.
%C If Y_i (i=1,2,3,4) are 2-blocks of an n-set X then, for n>=8, a(n-2) is the number of (n-3)-subsets of X intersecting each Y_i (i=1,2,3,4). - _Milan Janjic_, Nov 09 2007
%H G. C. Greubel, <a href="/A055809/b055809.txt">Table of n, a(n) for n = 4..1000</a>
%H Milan Janjic, <a href="https://pmf.unibl.org/wp-content/uploads/2017/10/enumfor.pdf">Two Enumerative Functions</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F For n>4, a(n) = n*(n^2 + 3*n - 22)/6.
%F G.f.: x^4*(1 + 11*x - 22*x^2 + 14*x^3 - 3*x^4)/(1-x)^4. - _Colin Barker_, Feb 22 2012
%F E.g.f.: x*(72 +48*x +8*x^2 -3*x^2 + (-72 +24*x +4*x^2)*exp(x))/24. - _G. C. Greubel_, Jan 23 2020
%p seq( `if`(n=4, 1, n*(n^2 +3*n -22)/6), n=4..50); # _G. C. Greubel_, Jan 23 2020
%t f[n_]:=Sum[i+i^2-8,{i,1,n}]/2;Table[f[n],{n,5,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 08 2010 *)
%t Table[If[n==4, 1, n*(n^2 +3*n -22)/6], {n,4,50}] (* _G. C. Greubel_, Jan 23 2020 *)
%o (PARI) Vec(x^4*(1 + 11*x - 22*x^2 + 14*x^3 - 3*x^4)/(1-x)^4 + O(x^50)) \\ _Michel Marcus_, Jan 10 2015
%o (PARI) vector(50, n, my(m=n+3); if(m==4, 1, m*(m^2 +3*m -22)/6)) \\ _G. C. Greubel_, Jan 23 2020
%o (Magma) [1] cat [n*(n^2 +3*n -22)/6: n in [5..50]]; // _G. C. Greubel_, Jan 23 2020
%o (Sage) [1]+[n*(n^2 +3*n -22)/6 for n in (5..50)] # _G. C. Greubel_, Jan 23 2020
%o (GAP) Concatenation([1], List([5..50], n-> n*(n^2 +3*n -22)/6 )); # _G. C. Greubel_, Jan 23 2020
%Y Cf. A055807, A055810, A055811, A055815, A055816, A055817.
%K nonn,easy
%O 4,2
%A _Clark Kimberling_, May 28 2000
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