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

0,2

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).

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

Mathematica

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

Prog

(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

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.

Sequence in context: A042918 A042920 A247438 * A116324 A179571 A044133

Adjacent sequences: A132769 A132770 A132771 * A132773 A132774 A132775

Keyword

nonn,easy

Author

Omar E. Pol, Aug 28 2007

Status

approved