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%I #36 Sep 08 2022 08:44:49
%S 1,3,8,21,54,133,309,674,1383,2683,4950,8735,14820,24285,38587,59652,
%T 89981,132771,192052,272841,381314,524997,712977,956134,1267395,
%U 1662011,2157858,2775763,3539856,4477949,5621943,7008264,8678329,10679043,13063328,15890685
%N a(n) = T(n, 2*n-7), T given by A027926.
%H G. C. Greubel, <a href="/A027930/b027930.txt">Table of n, a(n) for n = 4..1003</a>
%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) = Sum_{k=0..3} binomial(n-k, 7-2k). - _Len Smiley_, Oct 20 2001
%F a(n) = C(n-3,n-4)+C(n-2,n-5)+C(n-1,n-6)+C(n,n-7). - _Zerinvary Lajos_, May 29 2007
%F From _R. J. Mathar_, Oct 05 2009: (Start)
%F a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8).
%F G.f.: x^4*(1 - x + x^2)*(1 - 4*x + 7*x^2 - 4*x^3 + x^4)/(1-x)^8. (End)
%F From _G. C. Greubel_, Sep 06 2019: (Start)
%F a(n) = binomial(n-1, n-7) + (n-3)*((n-3)^4 + 15*(n-3)^2 + 104)/120.
%F E.g.f.: x*(5040 + 2520*x + 1680*x^2 + 630*x^3 + 168*x^4 + 21*x^5 + x^6)*exp(x)/5040. (End)
%p seq(binomial(n-3,n-4)+binomial(n-2,n-5)+binomial(n-1,n-6)+binomial(n,n-7) , n=4..50); # _Zerinvary Lajos_, May 29 2007
%t Table[Total[Binomial[First[#],Last[#]]&/@Table[{n+i,n-1-i},{i,0,3}]],{n,35}] (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1}, {1,3,8,21,54,133,309,674}, 35] (* _Harvey P. Dale_, Jun 23 2011 *)
%o (PARI) vector(40, n, binomial(n+3, n-4) + n*(n^4 +15*n^2 +104)/120) \\ _G. C. Greubel_, Sep 06 2019
%o (Magma) [Binomial(n-1, n-7) + (n-3)*((n-3)^4 +15*(n-3)^2 +104)/120: n in [4..40]]; // _G. C. Greubel_, Sep 06 2019
%o (Sage) [binomial(n-1, n-7) + (n-3)*((n-3)^4 +15*(n-3)^2 +104)/120 for n in (4..40)] # _G. C. Greubel_, Sep 06 2019
%o (GAP) List([4..40], n-> Binomial(n-1, n-7) + (n-3)*((n-3)^4 +15*(n-3)^2 +104)/120); # _G. C. Greubel_, Sep 06 2019
%Y Cf. A228074.
%K nonn,easy
%O 4,2
%A _Clark Kimberling_
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