A063521 a(n) = n*(7*n^2-4)/3.

0, 1, 16, 59, 144, 285, 496, 791, 1184, 1689, 2320, 3091, 4016, 5109, 6384, 7855, 9536, 11441, 13584, 15979, 18640, 21581, 24816, 28359, 32224, 36425, 40976, 45891, 51184, 56869, 62960, 69471, 76416, 83809, 91664, 99995, 108816, 118141

Offset

0,3

Comments

Also as a(n)=(1/6)*(14*n^3-8*n), n>0: structured heptagonal anti-diamond numbers (vertex structure 15) (Cf. A100186 = alternate vertex; A100188 = structured anti-diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov 07 2004

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+12*x+x^2)/(1-x)^4. - Colin Barker, Jan 10 2012

E.g.f.: (x/3)*(3 + 21*x + 7*x^2)*exp(x). - G. C. Greubel, Sep 01 2017

Maple

A063521:=n->n*(7*n^2-4)/3; seq(A063521(k), k=0..100); # Wesley Ivan Hurt, Oct 24 2013

Mathematica

lst={}; Do[AppendTo[lst, n*(7*n^2-4)/3], {n, 1, 6!}]; lst (* Vladimir Joseph Stephan Orlovsky, Sep 02 2008 *)
CoefficientList[Series[x*(1+12*x+x^2)/(1-x)^4, {x, 0, 50}], x] (* G. C. Greubel, Sep 01 2017 *)

Prog

(PARI) { for (n=0, 1000, write("b063521.txt", n, " ", n*(7*n^2 - 4)/3) ) } \\ Harry J. Smith, Aug 25 2009

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.

Sequence in context: A225922 A235510 A220974 * A027117 A292537 A258730

Adjacent sequences: A063518 A063519 A063520 * A063522 A063523 A063524

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 02 2001

Status

approved