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%I #27 Sep 06 2023 15:22:36
%S 0,1,17,63,154,305,531,847,1268,1809,2485,3311,4302,5473,6839,8415,
%T 10216,12257,14553,17119,19970,23121,26587,30383,34524,39025,43901,
%U 49167,54838,60929,67455,74431,81872,89793,98209,107135,116586
%N a(n) = n*(5*n^2 - 3)/2.
%H Harry J. Smith, <a href="/A063522/b063522.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 G.f.: x*(1 + 13*x + x^2)/(1-x)^4. - _Colin Barker_, Jan 10 2012
%F E.g.f.: (x/2)*(2 + 15*x + 5*x^2)*exp(x). - _G. C. Greubel_, Sep 01 2017
%t lst={};Do[AppendTo[lst, LegendreP[3, n]], {n, 10^2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 11 2008 *)
%t CoefficientList[Series[x*(1 + 13*x + x^2)/(1-x)^4, {x, 0, 50}], x] (* _G. C. Greubel_, Sep 01 2017 *)
%t LinearRecurrence[{4,-6,4,-1},{0,1,17,63},40] (* _Harvey P. Dale_, Sep 06 2023 *)
%o (PARI) { for (n=0, 1000, write("b063522.txt", n, " ", n*(5*n^2 - 3)/2) ) } \\ _Harry J. Smith_, Aug 25 2009
%o (Magma) [n*(5*n^2 -3)/2: n in [0..30]]; // _G. C. Greubel_, May 02 2018
%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.
%Y Bisections: A160674, A160699.
%K nonn,easy
%O 0,3
%A _N. J. A. Sloane_, Aug 02 2001
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