A098848 a(n) = n*(n + 14).

0, 15, 32, 51, 72, 95, 120, 147, 176, 207, 240, 275, 312, 351, 392, 435, 480, 527, 576, 627, 680, 735, 792, 851, 912, 975, 1040, 1107, 1176, 1247, 1320, 1395, 1472, 1551, 1632, 1715, 1800, 1887, 1976, 2067, 2160, 2255, 2352, 2451, 2552, 2655, 2760, 2867

Offset

0,2

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).

Formula

a(n) = (n+7)^2 - 7^2 = n*(n + 14), n>=0.

G.f.: x*(15 - 13*x)/(1-x)^3.

a(n) = 2*n + a(n-1) + 13 (with a(0)=0). - Vincenzo Librandi, Nov 16 2010

Sum_{n>=1} 1/a(n) = 1171733/5045040 = 0.2322544518... via Sum_{n>=0} 1/((n+x)(n+y)) = (psi(x)-psi(y))/(x-y). - R. J. Mathar, Jul 14 2012

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*(15 + x)*exp(x). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = 237371/5045040. - Amiram Eldar, Jan 15 2021

Mathematica

Table[ n(n + 14), {n, 0, 50}] (* Robert G. Wilson v, Jul 14 2005 *)
LinearRecurrence[{3, -3, 1}, {0, 15, 32}, 50] (* G. C. Greubel, Jul 29 2016 *)

Prog

(PARI) a(n)=n*(n+14) \\ Charles R Greathouse IV, Sep 24 2015

Crossrefs

Cf. A098832.

a(n-7), n>=8, seventh column (used for the n=7 series of the hydrogen atom) of triangle A120070.

Sequence in context: A157767 A146889 A061047 * A055809 A112147 A007256

Adjacent sequences: A098845 A098846 A098847 * A098849 A098850 A098851

Keyword

nonn,easy

Author

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

Extensions

More terms from Robert G. Wilson v, Jul 14 2005

Status

approved