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

 

Logo

Annual Appeal: Please make a donation (tax deductible in USA) to keep the OEIS running. Over 5000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A168566 a(n) = (n-1)*(n+2)*(n^2 + n + 2)/4. 1
0, 8, 35, 99, 224, 440, 783, 1295, 2024, 3024, 4355, 6083, 8280, 11024, 14399, 18495, 23408, 29240, 36099, 44099, 53360, 64008, 76175, 89999, 105624, 123200, 142883, 164835, 189224, 216224, 246015, 278783, 314720, 354024, 396899, 443555, 494208 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The products of two consecutive numbers in this sequence may be evaluated in terms of the Frobenius numbers for 5 consecutive integers, A138985(n) = F(n): for n>0, a(2n-1)*a(2n) = F(4n^2-2)^2 - (2n)^2; a(2n)*a(2n+1) = F(4n^2+4n)^2 - (2n+1)^2. - Charlie Marion, Jan 23 2012

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

FORMULA

G.f.: x^2*(-8 + 5*x - 4*x^2 + x^3)/(x-1)^5. - R. J. Mathar, Jan 04 2011

a(n) = A000217(n)^2 - 1. - Charlie Marion, Sep 27 2011

From G. C. Greubel, Jul 26 2016: (Start)

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

E.g.f.: (1/4)*(4 - (4 - 4*x + 14*x^2 + 8*x^3)*exp(x)). (End)

MATHEMATICA

s=0; lst={s}; Do[s+=n^3; AppendTo[lst, s], {n, 2, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Apr 27 2010 *)

Table[(n-1)*(n+2)*(n^2 + n + 2)/4, {n, 1, 25}] (* G. C. Greubel, Jul 26 2016 *)

PROG

(MAGMA) [(n-1)*(n+2)*(n^2+n+2)/4: n in [1..50]]

(PARI) a(n)=(n-1)*(n+2)*(n^2+n+2)/4 \\ Charles R Greathouse IV, Jul 26 2016

CROSSREFS

Cf. A000578 (first differences).

Sequence in context: A100907 A265840 A212903 * A058102 A212674 A189592

Adjacent sequences:  A168563 A168564 A168565 * A168567 A168568 A168569

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Nov 30 2009

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 December 10 03:42 EST 2016. Contains 278993 sequences.