A017018 a(n) = (7*n + 3)^2.

9, 100, 289, 576, 961, 1444, 2025, 2704, 3481, 4356, 5329, 6400, 7569, 8836, 10201, 11664, 13225, 14884, 16641, 18496, 20449, 22500, 24649, 26896, 29241, 31684, 34225, 36864, 39601, 42436, 45369, 48400

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A017017.

Programs

Magma

[(7*n+3)^2: n in [0..35]]; // Vincenzo Librandi, Jul 14 2011

Mathematica

(7*Range[0,40]+3)^2 (* or *) LinearRecurrence[{3,-3,1},{9,100,289},40] (* Harvey P. Dale, Jul 19 2014 *)

PARI

a(n)=(7*n+3)^2 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[(7*n+3)^2 for n in range(40)] # G. C. Greubel, Oct 17 2023

Formula

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3); a(0)=9, a(1)=100, a(2)=289. - Harvey P. Dale, Jul 19 2014

G.f.: (9 + 73*x + 16*x^2)/(1-x)^3. - Harvey P. Dale, Jul 19 2014

E.g.f.: (9 + 91*x + 49*x^2)*exp(x). - G. C. Greubel, Oct 17 2023

Sum_{n>=0} 1/a(n) = psi'(3/7)/49 = 0.13147479209450263890925... - R. J. Mathar, May 07 2024