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!)
A079547 ((n^6-(n-1)^6)-(n^2-(n-1)^2))/60. 13
0, 1, 11, 56, 192, 517, 1183, 2408, 4488, 7809, 12859, 20240, 30680, 45045, 64351, 89776, 122672, 164577, 217227, 282568, 362768, 460229, 577599, 717784, 883960, 1079585, 1308411 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Polynexus numbers of order 6.

A polynexus (subtractive) function is composed of two or more subtracted nexus numbers divided by an integer x. The general form of the formula is a(n)=((n^p-(n-1)^p)-(n^q-(n-1)^q))/x, where n, p, q and x are integers.

Already known: ((n^5-(n-1)^5)-(n^3-(n-1)^3))/24, giving A006322 for n>1; ((n^4-(n-1)^4)-(n^2-(n-1)^2))/12, giving A000330; ((n^3-(n-1)^3)-(n^1-(n-1)^1))/6, giving A000217; ((n^2-(n-1)^2)-(n^1-(n-1)^1))/2, giving n; ((n^2-(n-1)^2)-(n^0-(n-1)^0))/1, giving 2*n-1. In those examples, x is equal to 1,2,6,12,24, and 3 is also possible.

Also number of monotone n-weightings of complete bipartite digraph K(3,2) if offset were 0; cf. A085464-A085465. - Goran Kilibarda, Vladeta Jovovic, Jul 01 2003

Partial sums of A037270. - J. M. Bergot, Jun 07 2012

LINKS

Bruno Berselli, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

FORMULA

a(n+1) = sum(i=1..n) (i^2 + i^4)/2 = n*(2*n+1)*(n+1)*(3*n^2+3*n+4)/60. - Vladeta Jovovic, Mar 17 2006

G.f.: x^2*(x+1)*(1+4*x+x^2)/(1-x)^6. - Bruno Berselli, Feb 13 2012

a(n) = sum(i=1..n-1, sum (j=1..n-1, min(i,j)^3)). - Enrique Pérez Herrero, Jan 16 2013

MATHEMATICA

Table[((n^6 - (n - 1)^6) - (n^2 - (n - 1)^2))/60, {n, 27}] (* Bruno Berselli, Feb 13 2012 *)

PROG

(PARI) n*(6*n^4-15*n^3+20*n^2-15*n+4)/60 \\ Charles R Greathouse IV, Jan 16 2013

CROSSREFS

Cf. A006322, A000330, A000217, A047969, A003215, A083200, A088889-A088894.

Sequence in context: A275643 A223773 A224154 * A034264 A051946 A224405

Adjacent sequences:  A079544 A079545 A079546 * A079548 A079549 A079550

KEYWORD

nonn,easy

AUTHOR

Xavier Acloque, Jan 22 2003

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 7 05:39 EST 2016. Contains 278841 sequences.