login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A063489 a(n) = (2*n-1)*(5*n^2-5*n+6)/6. 17
1, 8, 30, 77, 159, 286, 468, 715, 1037, 1444, 1946, 2553, 3275, 4122, 5104, 6231, 7513, 8960, 10582, 12389, 14391, 16598, 19020, 21667, 24549, 27676, 31058, 34705, 38627, 42834, 47336, 52143, 57265, 62712, 68494, 74621, 81103, 87950 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Harry J. Smith, 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

G.f.: x*(1+x)*(1+3*x+x^2)/(1-x)^4. - Colin Barker, Mar 02 2012

a(n) = 4*a(n-1) -6*a(n-2) +4*a(n-3) -a(n-4), with a(1)=1, a(2)=8, a(3)=30, a(4)=77. - Harvey P. Dale, Aug 20 2012

E.g.f.: (-6 + 12*x + 15*x^2 + 10*x^3)*exp(x)/6 + 1. - G. C. Greubel, Dec 01 2017

MATHEMATICA

Table[(2n-1)(5n^2-5n+6)/6, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {1, 8, 30, 77}, 40] (* Harvey P. Dale, Aug 20 2012 *)

PROG

(PARI) { for (n=1, 1000, write("b063489.txt", n, " ", (2*n - 1)*(5*n^2 - 5*n + 6)/6) ) } \\ Harry J. Smith, Aug 23 2009

(MAGMA) [(2*n-1)*(5*n^2-5*n+6)/6: n in [1..30]]; // G. C. Greubel, Dec 01 2017

(PARI) x='x+O('x^30); Vec(serlaplace((-6 + 12*x + 15*x^2 + 10*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: A055832 A195753 A100175 * A002417 A126858 A232772

Adjacent sequences:  A063486 A063487 A063488 * A063490 A063491 A063492

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Aug 01 2001

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified January 17 16:33 EST 2018. Contains 297822 sequences.