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%I #16 Jan 25 2019 17:25:09
%S 0,8,21,40,66,100,143,196,260,336,425,528,646,780,931,1100,1288,1496,
%T 1725,1976,2250,2548,2871,3220,3596,4000,4433,4896,5390,5916,6475,
%U 7068,7696,8360,9061,9800,10578,11396,12255,13156,14100,15088,16121,17200,18326,19500,20723,21996
%N a(n) = (n-4)*(n+1)*(n+3)/6.
%H Colin Barker, <a href="/A275874/b275874.txt">Table of n, a(n) for n = 4..1000</a>
%H Hilton, Peter John, and Jean Pedersen, <a href="https://www.e-periodica.ch/digbib/view?pid=ens-001:1981:27::136#485">Descartes, Euler, Poincaré, Pólya and Polyhedra</a>, L'Enseign. Math., 27 (1981), 327-343. See Cor. 1.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F From _Colin Barker_, Aug 15 2016: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n > 7.
%F G.f.: x^5*(8 - 11*x + 4*x^2) / (1 - x)^4.
%F (End)
%p a := n -> (n - 4)*(n + 1)*(n + 3)/6:
%p seq(a(n), n = 4..51); # _Peter Luschny_, Jan 25 2019
%o (PARI) concat(0, Vec(x^5*(8-11*x+4*x^2)/(1-x)^4 + O(x^50))) \\ _Colin Barker_, Aug 15 2016
%Y A137742 is an essentially identical sequence.
%K nonn,easy
%O 4,2
%A _N. J. A. Sloane_, Aug 14 2016
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