OFFSET
0,3
LINKS
Harry J. Smith, Table of n, a(n) for n = 0..1000
T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (11).
Index entries for linear recurrences with constant coefficients, signature (4, -6, 4, -1).
FORMULA
G.f.: x*(1 + 13*x + x^2)/(1-x)^4. - Colin Barker, Jan 10 2012
E.g.f.: (x/2)*(2 + 15*x + 5*x^2)*exp(x). - G. C. Greubel, Sep 01 2017
MATHEMATICA
lst={}; Do[AppendTo[lst, LegendreP[3, n]], {n, 10^2}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 11 2008 *)
CoefficientList[Series[x*(1 + 13*x + x^2)/(1-x)^4, {x, 0, 50}], x] (* G. C. Greubel, Sep 01 2017 *)
LinearRecurrence[{4, -6, 4, -1}, {0, 1, 17, 63}, 40] (* Harvey P. Dale, Sep 06 2023 *)
PROG
(PARI) a(n) = { n*(5*n^2 - 3)/2 } \\ Harry J. Smith, Aug 25 2009
(Magma) [n*(5*n^2 -3)/2: n in [0..30]]; // G. C. Greubel, May 02 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Aug 02 2001
STATUS
approved