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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A036659 Product of n with sum of next n consecutive integers. 6
2, 14, 45, 104, 200, 342, 539, 800, 1134, 1550, 2057, 2664, 3380, 4214, 5175, 6272, 7514, 8910, 10469, 12200, 14112, 16214, 18515, 21024, 23750, 26702, 29889, 33320, 37004, 40950, 45167, 49664, 54450, 59534, 64925, 70632, 76664 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 2 + (3*n*n + 10*n + 11)*n/2. - Frank Ellermann, Mar 16 2002

a(n) = n^2(3n + 1)/2. - Ronnie B Kon (ronniekon(AT)yahoo.com), Jun 09 2006

G.f.: x*(2 + 6*x + x^2)/(1 - x)^4. - Colin Barker, Mar 27 2012

EXAMPLE

n=3 -> 3*(4+5+6)=45

MATHEMATICA

CoefficientList[Series[(2+6*x+x^2)/(1-x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Apr 25 2012 *)

Table[(n^2*(1+3n))/2, {n, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {2, 14, 45, 104}, 40] (* Harvey P. Dale, Jan 04 2015 *)

PROG

(PARI) a(n)=n^2*(3*n+1)/2 \\ Charles R Greathouse IV, Dec 08 2011

(MAGMA) I:=[2, 14, 45, 104]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Apr 25 2012

CROSSREFS

Cf. A036660.

Sequence in context: A085929 A231247 A318764 * A079937 A324915 A281760

Adjacent sequences:  A036656 A036657 A036658 * A036660 A036661 A036662

KEYWORD

nonn,easy

AUTHOR

G. L. Honaker, Jr., Dec 15 1998

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 21 05:02 EDT 2021. Contains 347596 sequences. (Running on oeis4.)