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

Author

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

Keywords

• nonn
• easy

Examples

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

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).

Crossrefs

Cf. A036660.

Programs

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

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 *)

PARI

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

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)