A140679 a(n) = n*(3*n+14).

0, 17, 40, 69, 104, 145, 192, 245, 304, 369, 440, 517, 600, 689, 784, 885, 992, 1105, 1224, 1349, 1480, 1617, 1760, 1909, 2064, 2225, 2392, 2565, 2744, 2929, 3120, 3317, 3520, 3729, 3944, 4165, 4392, 4625, 4864, 5109, 5360, 5617, 5880, 6149, 6424, 6705, 6992

Offset: 0

Author

Omar E. Pol, May 22 2008

Keywords

• easy
• nonn
• changed

Examples

			a(1)=6*1+0+11=17; a(2)=6*2+17+11=40; a(3)=6*3+40+11=69. See 2nd formula.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 0..5000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A033428, A045944, A140676, A067725, A140677, A140678, A067707, A140680, A140681, A140689.

Programs

Mathematica

Table[n(3n+14),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,17,40},50] (* Harvey P. Dale, Apr 29 2011 *)

PARI

a(n)=n*(3*n+14) \\ Charles R Greathouse IV, Oct 07 2015

Formula

a(n) = 3*n^2 + 14*n.

a(n) = a(n-1) + 6*n + 11, with a(0)=0. - Vincenzo Librandi, Aug 03 2010

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3), with a(1)=0, a(2)=17, a(3)=40. - Harvey P. Dale, Apr 29 2011

E.g.f.: (3*x^2 + 17*x)*exp(x). - G. C. Greubel, Jul 20 2017