The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Please make a donation to keep the OEIS running. We are now in our 56th year. In the past year we added 10000 new sequences and reached almost 9000 citations (which often say "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A086755 Sum_{k=1..n} (k(k+1))^2/2. 0
 2, 20, 92, 292, 742, 1624, 3192, 5784, 9834, 15884, 24596, 36764, 53326, 75376, 104176, 141168, 187986, 246468, 318668, 406868, 513590, 641608, 793960, 973960, 1185210, 1431612, 1717380, 2047052, 2425502, 2857952, 3349984, 3907552 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1). FORMULA (n+1)(n+2)(n+3)(3n^2+12n+10)/30 = 2*A024166(n+1). G.f. 2*(1+4*x+x^2) / (x-1)^6 . - R. J. Mathar, Sep 15 2012 EXAMPLE a(3)=(1*2)^2/2+(2*3)^2/2+(3.4)^2/2=2+18+72=92 MATHEMATICA Table[Sum[(k(k+1))^2/2, {k, n}], {n, 40}] (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {2, 20, 92, 292, 742, 1624}, 40] (* Harvey P. Dale, Oct 04 2020 *) PROG (PARI) for(i=1, 20, print1(", "sum(j=1, i, (j*(j+1))^2/2))) CROSSREFS Sequence in context: A069187 A328510 A033840 * A107483 A220856 A035599 Adjacent sequences:  A086752 A086753 A086754 * A086756 A086757 A086758 KEYWORD nonn,easy AUTHOR Jon Perry, Jul 31 2003 EXTENSIONS More terms from Jason Earls, Aug 01 2003 Definition clarified by Harvey P. Dale, Oct 04 2020 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
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified November 28 11:02 EST 2020. Contains 338720 sequences. (Running on oeis4.)