%I #17 Sep 08 2022 08:44:49
%S 1,2,5,13,34,88,221,530,1204,2587,5270,10220,18955,33775,58060,96647,
%T 156299,246280,379051,571103,843944,1225258,1750255,2463232,3419366,
%U 4686761,6348772,8506630,11282393,14822249,19300198,24922141
%N T(n, 2n-8), T given by A027926.
%H G. C. Greubel, <a href="/A027931/b027931.txt">Table of n, a(n) for n = 4..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) = Sum_{k=0..4} binomial(n-k, 8-2*k). - _Len Smiley_, Oct 20 2001
%F G.f.: x^4*(1 -7*x +23*x^2 -44*x^3 +55*x^4 -44*x^5 +23*x^6 -7*x^7+ x^8) / (1-x)^9 . - _R. J. Mathar_, Oct 31 2015
%p A027931 := proc(n)
%p add(binomial(n-k,8-2*k),k=0..4) ;
%p end proc: # _R. J. Mathar_, Oct 31 2015
%t Sum[Binomial[Range[4,40] -k, 8-2*k], {k,0,4}] (* _G. C. Greubel_, Sep 27 2019 *)
%o (PARI) vector(40, n, sum(k=0,4, binomial(n+3-k, 8-2*k)) ) \\ _G. C. Greubel_, Sep 27 2019
%o (Magma) [&+[Binomial(n-k, 8-2*k): k in [0..4]] : n in [4..40]]; // _G. C. Greubel_, Sep 27 2019
%o (Sage) [sum(binomial(n-k, 8-2*k) for k in (0..4)) for n in (4..40)] # _G. C. Greubel_, Sep 27 2019
%o (GAP) List([4..40], n-> Sum([0..4], k-> Binomial(n-k, 8-2*k)) ); # _G. C. Greubel_, Sep 27 2019
%Y Cf. A027926, A228074.
%K nonn,easy
%O 4,2
%A _Clark Kimberling_