A036659 Product of n with sum of next n consecutive integers.

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, 83030, 89739, 96800, 104222, 112014

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

From Amiram Eldar, Jan 10 2023: (Start)

Sum_{n>=1} 1/a(n) = Pi^2/3 + sqrt(3)*Pi + 9*log(3) - 18.

Sum_{n>=1} (-1)^(n+1)/a(n) = Pi^2/6 - 2*sqrt(3)*Pi - 12*log(2) + 18. (End)

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