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%I #15 Sep 08 2022 08:46:17
%S 0,-4,-8,-4,16,60,136,252,416,636,920,1276,1712,2236,2856,3580,4416,
%T 5372,6456,7676,9040,10556,12232,14076,16096,18300,20696,23292,26096,
%U 29116,32360,35836,39552,43516,47736,52220,56976,62012,67336,72956,78880,85116,91672,98556,105776,113340,121256
%N a(n) = 4*n*(n^2 - 3*n - 1)/3.
%H Colin Barker, <a href="/A275876/b275876.txt">Table of n, a(n) for n = 0..1000</a>
%H Peter John Hilton and Jean Pedersen, <a href="http://dx.doi.org/10.5169/seals-51756">Descartes, Euler, Poincaré, Pólya and Polyhedra</a>, L'Enseign. Math., 27 (1981), 327-343. See Cor. 2.
%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>3.
%F G.f.: -4*x*(1-2*x-x^2) / (1-x)^4. (End)
%F E.g.f.: 4*x*(-3 + x^2)*exp(x)/3. - _G. C. Greubel_, Apr 28 2019
%t LinearRecurrence[{4,-6,4,-1}, {0,-4,-8,-4}, 50] (* _G. C. Greubel_, Apr 28 2019 *)
%o (PARI) concat(0, Vec(-4*x*(1-2*x-x^2)/(1-x)^4 + O(x^50))) \\ _Colin Barker_, Aug 15 2016
%o (Magma) [4*n*(n^2-3*n-1)/3: n in [0..50]]; // _G. C. Greubel_, Apr 28 2019
%o (Sage) [4*n*(n^2-3*n-1)/3 for n in (0..50)] # _G. C. Greubel_, Apr 28 2019
%o (GAP) List([0..50], n-> 4*n*(n^2-3*n-1)/3) # _G. C. Greubel_, Apr 28 2019
%K sign,easy
%O 0,2
%A _N. J. A. Sloane_, Aug 14 2016