A132766 a(n) = n*(n+24).

0, 25, 52, 81, 112, 145, 180, 217, 256, 297, 340, 385, 432, 481, 532, 585, 640, 697, 756, 817, 880, 945, 1012, 1081, 1152, 1225, 1300, 1377, 1456, 1537, 1620, 1705, 1792, 1881, 1972, 2065, 2160, 2257, 2356, 2457, 2560, 2665, 2772, 2881, 2992, 3105, 3220, 3337

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) = n*(n + 24).

a(n) = 2*n + a(n-1) + 23 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010

a(0)=0, a(1)=25, a(2)=52; for n>2, a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Harvey P. Dale, Feb 11 2016

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(24)/24 = A001008(24)/A102928(24) = 1347822955/8566766208, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 3602044091/128501493120. (End)

From G. C. Greubel, Mar 14 2022: (Start)

G.f.: 2*x*(13 - 12*x)/(1-x)^3.

E.g.f.: x*(26 + x)*exp(x). (End)

Mathematica

Table[n (n + 24), {n, 0, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {0, 25, 52}, 50] (* Harvey P. Dale, Feb 11 2016 *)

Prog

(PARI) a(n)=n*(n+24) \\ Charles R Greathouse IV, Jun 17 2017
(Sage) [n*(n+24) for n in (0..50)] # G. C. Greubel, Mar 14 2022

Crossrefs

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

Sequence in context: A042244 A042246 A042248 * A039412 A352260 A199990

Adjacent sequences: A132763 A132764 A132765 * A132767 A132768 A132769

Keyword

easy,nonn

Author

Omar E. Pol, Aug 28 2007

Status

approved