A132765 a(n) = n*(n + 23).

0, 24, 50, 78, 108, 140, 174, 210, 248, 288, 330, 374, 420, 468, 518, 570, 624, 680, 738, 798, 860, 924, 990, 1058, 1128, 1200, 1274, 1350, 1428, 1508, 1590, 1674, 1760, 1848, 1938, 2030, 2124, 2220, 2318, 2418, 2520, 2624, 2730, 2838, 2948, 3060, 3174, 3290, 3408

Offset: 0

Author

Omar E. Pol, Aug 28 2007

Keywords

• nonn
• easy

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, ResearchGate, 2014.
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A001008, A001477, A002378, A005563, A028347, A028552, A028557, A028560, A028563, A028566, A028569, A056126, A098603, A098847, A098848, A098849, A098850, A102928, A120071, A132759, A132760, A132761, A132762, A132763, A132764, A132765, A132766.

Programs

Mathematica

Table[n (n + 23), {n, 0, 50}] (* Bruno Berselli, Sep 03 2018 *)

PARI

a(n)=n*(n+23) \\ Charles R Greathouse IV, Jun 17 2017

Sage

[n*(n+23) for n in (0..50)] # G. C. Greubel, Mar 14 2022

Formula

a(n) = n*(n + 23).

a(n) = 2*n + a(n-1) + 22 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*(12 - 11*x)/(1-x)^3. (End)

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(23)/23 = A001008(23)/A102928(23) = 444316699/2736605872, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/23 - 3825136961/123147264240. (End)

E.g.f.: x*(24 + x)*exp(x). - G. C. Greubel, Mar 14 2022