A049480 a(n) = (2*n-1)*(n^2 -n +6)/6.

1, 4, 10, 21, 39, 66, 104, 155, 221, 304, 406, 529, 675, 846, 1044, 1271, 1529, 1820, 2146, 2509, 2911, 3354, 3840, 4371, 4949, 5576, 6254, 6985, 7771, 8614, 9516, 10479, 11505, 12596, 13754, 14981, 16279, 17650, 19096, 20619, 22221

Offset

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

T. P. Martin, Shells of atoms, Phys. Rep., 273 (1996), 199-241, eq. (10).

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

From Harvey P. Dale, Jan 01 2012: (Start)

G.f.: x*(x^3 + 1)/(x-1)^4.

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4); a(1)=1, a(2)=4, a(3)=10, a(4)=21. (End)

E.g.f.: (-6 + 12*x + 3*x^2 + 2*x^3)*exp(x)/6 + 1. - G. C. Greubel, Dec 01 2017

Mathematica

Table[(2n-1)(n^2-n+6)/6, {n, 50}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 4, 10, 21}, 50] (* Harvey P. Dale, Jan 01 2012 *)

Prog

(PARI) a(n)=(2*n-1)*(n^2-n+6)/6 \\ Charles R Greathouse IV, Sep 24 2015
(Magma) [(2*n-1)*(n^2-n+6)/6: n in [1..30]]; // G. C. Greubel, Dec 01 2017
(PARI) x='x+O('x^30); Vec(serlaplace((-6 + 12*x + 3*x^2 + 2*x^3)*exp(x)/6 + 1)) \\ G. C. Greubel, Dec 01 2017

Crossrefs

1/12*t*(2*n^3-3*n^2+n)+2*n-1 for t = 2, 4, 6, ... gives A049480, A005894, A063488, A001845, A063489, A005898, A063490, A057813, A063491, A005902, A063492, A005917, A063493, A063494, A063495, A063496.

Sequence in context: A008121 A253687 A253688 * A216172 A055908 A325951

Adjacent sequences: A049477 A049478 A049479 * A049481 A049482 A049483

Keyword

nonn,easy

Author

N. J. A. Sloane, Aug 01 2001

Status

approved