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A132765 a(n) = n*(n + 23). 17
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 (list; graph; refs; listen; history; text; internal format)
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, ResearchGate, 2014.

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

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

MATHEMATICA

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

PROG

(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

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.

Sequence in context: A042148 A042150 A087355 * A274898 A025137 A070197

Adjacent sequences:  A132762 A132763 A132764 * A132766 A132767 A132768

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Aug 28 2007

STATUS

approved

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Last modified August 17 05:07 EDT 2022. Contains 356184 sequences. (Running on oeis4.)