A132772 a(n) = n*(n + 30).

0, 31, 64, 99, 136, 175, 216, 259, 304, 351, 400, 451, 504, 559, 616, 675, 736, 799, 864, 931, 1000, 1071, 1144, 1219, 1296, 1375, 1456, 1539, 1624, 1711, 1800, 1891, 1984, 2079, 2176, 2275, 2376, 2479, 2584, 2691, 2800, 2911, 3024, 3139, 3256, 3375, 3496, 3619

Offset: 0

Author

Omar E. Pol, Aug 28 2007

Keywords

• nonn
• easy

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566.

Cf. A028569, A067079, A098849, A098850, A098603, A098847, A098848, A102928, A120071.

Cf. A132759, A132760, A132761, A132762, A132763, A132764, A132765, A132766, A132767.

Cf. A132768, A132769, A132770, A132771.

Programs

Mathematica

Table[n(n+30),{n,0,50}] (* or *) LinearRecurrence[{3,-3,1},{0,31,64},50] (* Harvey P. Dale, Mar 06 2015 *)

PARI

a(n)=n*(n+30) \\ Charles R Greathouse IV, Jun 17 2017

Sage

[n*(n+30) for n in (0..50)] # G. C. Greubel, Mar 13 2022

Formula

G.f.: x*(31-29*x)/(1-x)^3. - R. J. Mathar, Nov 14 2007

a(n) = 2*n + a(n-1) + 29 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(0)=0, a(1)=31, a(2)=64, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Mar 06 2015

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(30)/30 = A001008(30)/A102928(30) = 9304682830147/69872686884000, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 225175759291/9981812412000. (End)

E.g.f.: x*(31 + x)*exp(x). - G. C. Greubel, Mar 13 2022