A063522 a(n) = n*(5*n^2 - 3)/2.

0, 1, 17, 63, 154, 305, 531, 847, 1268, 1809, 2485, 3311, 4302, 5473, 6839, 8415, 10216, 12257, 14553, 17119, 19970, 23121, 26587, 30383, 34524, 39025, 43901, 49167, 54838, 60929, 67455, 74431, 81872, 89793, 98209, 107135, 116586, 126577, 137123, 148239, 159940

Offset: 0

Author

N. J. A. Sloane, Aug 02 2001

Keywords

• nonn
• easy

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).

Crossrefs

(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.

Bisections: A160674, A160699.

Programs

Magma

[n*(5*n^2 -3)/2: n in [0..30]]; // G. C. Greubel, May 02 2018

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 *)

PARI

a(n) = { n*(5*n^2 - 3)/2 } \\ Harry J. Smith, Aug 25 2009

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