A098850 a(n) = n*(n + 18).

0, 19, 40, 63, 88, 115, 144, 175, 208, 243, 280, 319, 360, 403, 448, 495, 544, 595, 648, 703, 760, 819, 880, 943, 1008, 1075, 1144, 1215, 1288, 1363, 1440, 1519, 1600, 1683, 1768, 1855, 1944, 2035, 2128, 2223, 2320, 2419, 2520, 2623, 2728, 2835, 2944, 3055

Offset: 0

Author

Eugene McDonnell (eemcd(AT)mac.com), Nov 04 2004

Keywords

• nonn
• easy

Links

• G. C. Greubel, 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).

Crossrefs

Cf. A001008, A098832, A102928.

a(n-9), n>=10, ninth column (used for the n=9 series of the hydrogen atom) of triangle A120070.

Programs

Maple

seq(n*(n+18),n=0..52); # Emeric Deutsch, Mar 06 2005

Mathematica

LinearRecurrence[{3, -3, 1}, {0, 19, 40}, 25] (* G. C. Greubel, Jul 29 2016 *)

PARI

a(n)=n*(n+18) \\ Charles R Greathouse IV, Jun 17 2017

Formula

a(n) = (n+9)^2 - 9^2 = n*(n + 18), n>=0.

G.f.: x*(19 - 17*x)/(1-x)^3.

a(n) = 2*n + a(n-1) + 17 (with a(0)=0). - Vincenzo Librandi, Nov 17 2010

From G. C. Greubel, Jul 29 2016: (Start)

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

E.g.f.: x*(19 + x)*exp(x). (End)

From Amiram Eldar, Jan 16 2021: (Start)

Sum_{n>=1} 1/a(n) = H(18)/18 = A001008(18)/A102928(18) = 14274301/73513440, where H(k) is the k-th harmonic number.

Sum_{n>=1} (-1)^(n+1)/a(n) = 1632341/44108064. (End)

Extensions

More terms from Emeric Deutsch, Mar 06 2005