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!)
A086689 a(n) = Sum_{i=1..n} i^2*t(i), where t = A000217. 1
1, 13, 67, 227, 602, 1358, 2730, 5034, 8679, 14179, 22165, 33397, 48776, 69356, 96356, 131172, 175389, 230793, 299383, 383383, 485254, 607706, 753710, 926510, 1129635, 1366911, 1642473, 1960777, 2326612, 2745112 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

This sequence is related to A001296 by a(n) = n*A001296(n) - Sum_{i=0..n-1} A001296(i) with n>0. - Bruno Berselli, Jan 21 2013

LINKS

Vincenzo Librandi, 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) = n*(n+1)*(n+2)*(12*n^2+9*n-1)/120.

G.f. x*(1+7*x+4*x^2) / (x-1)^6. - R. J. Mathar, Sep 15 2012

a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Wesley Ivan Hurt, Nov 19

a(n) = Sum_{i=1..n} ( i*Sum_{k=1..i} i*k ). - Wesley Ivan Hurt, Nov 19 2014

EXAMPLE

a(4) = 227 = 1^2*A000217(1)+2^2*A000217(2)+3^2*A000217(3)+4^2*A000217(4).

MAPLE

A086689:=n->n*(n+1)*(n+2)*(12*n^2+9*n-1)/120: seq(A086689(n), n=1..40); # Wesley Ivan Hurt, Nov 19 2014

MATHEMATICA

Table[n (n + 1) (n + 2) (12 n^2 + 9 n - 1)/120, {n, 40}] (* Wesley Ivan Hurt, Nov 19 2014 *)

CoefficientList[Series[(1 + 7 x + 4 x^2) / (x - 1)^6, {x, 0, 50}], x] (° Vincenzo Librandi, Nov 20 2014 °)

PROG

(PARI) t(n)=n*(n+1)/2 for(i=1, 30, print1(", "sum(j=1, i, j^2*t(i))))

(MAGMA) [n*(n+1)*(n+2)*(12*n^2+9*n-1)/120 : n in [1..40]]; // Wesley Ivan Hurt, Nov 19 2014

CROSSREFS

Cf. A001296.

Sequence in context: A067863 A257809 A106975 * A141956 A137720 A199896

Adjacent sequences:  A086686 A086687 A086688 * A086690 A086691 A086692

KEYWORD

nonn,easy

AUTHOR

Jon Perry, Jul 28 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 6 06:58 EST 2016. Contains 278775 sequences.