A132762 a(n) = n*(n + 19).

0, 20, 42, 66, 92, 120, 150, 182, 216, 252, 290, 330, 372, 416, 462, 510, 560, 612, 666, 722, 780, 840, 902, 966, 1032, 1100, 1170, 1242, 1316, 1392, 1470, 1550, 1632, 1716, 1802, 1890, 1980, 2072, 2166, 2262, 2360, 2460, 2562, 2666, 2772, 2880, 2990, 3102, 3216

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..5000

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

a(n) = 2*n + a(n-1) + 18 for n > 0, a(0) = 0. - Vincenzo Librandi, Aug 03 2010

From Chai Wah Wu, Dec 17 2016: (Start)

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2.

G.f.: 2*x*(10 - 9*x)/(1-x)^3. (End)

a(n) = 2*A051942(n+9). - R. J. Mathar, Sep 05 2018

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(19)/19 = A001008(19)/A102928(19) = 275295799/1474352880, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/19 - 33464927/884611728. (End)

E.g.f.: x*(20 + x)*exp(x). - G. C. Greubel, Mar 14 2022

Mathematica

Table[n (n + 19), {n, 0, 50}] (* Bruno Berselli, Sep 05 2018 *)
LinearRecurrence[{3, -3, 1}, {0, 20, 42}, 60] (* Harvey P. Dale, Jun 03 2021 *)

Prog

(PARI) a(n)=n*(n+19) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+19) for n in (0..50)] # G. C. Greubel, Mar 14 2022

Crossrefs

Cf. A001008, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A051942, A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761, A132763, A132764, A132765, A132766, A132767.

Sequence in context: A041794 A041796 A041798 * A075228 A256102 A128672

Adjacent sequences: A132759 A132760 A132761 * A132763 A132764 A132765

Keyword

nonn,easy

Author

Omar E. Pol, Aug 28 2007

Status

approved