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%I #17 Oct 18 2022 15:00:44
%S 0,1,15,55,134,265,461,735,1100,1569,2155,2871,3730,4745,5929,7295,
%T 8856,10625,12615,14839,17310,20041,23045,26335,29924,33825,38051,
%U 42615,47530,52809,58465,64511,70960,77825,85119,92855,101046,109705
%N a(n) = n*(13*n^2 - 7)/6.
%H Harry J. Smith, <a href="/A062025/b062025.txt">Table of n, a(n) for n = 0..1000</a>
%H T. P. Martin, <a href="http://dx.doi.org/10.1016/0370-1573(95)00083-6">Shells of atoms</a>, Phys. Reports, 273 (1996), 199-241, eq. (11).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4, -6, 4, -1).
%F From _G. C. Greubel_, Sep 01 2017: (Start)
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
%F G.f.: (x + 11*x^2 + x^3)/(1 - x)^4.
%F E.g.f.: (x/6)*(6 + 39*x + 13*x^2)*exp(x). (End)
%t Table[n(13n^2-7)/6,{n,0,80}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 18 2011 *)
%o (PARI) for (n=0, 1000, write("b062025.txt", n, " ", n*(13*n^2 - 7)/6) ) \\ _Harry J. Smith_, Jul 29 2009
%Y 1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Aug 02 2001
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