A016922 a(n) = (6*n+1)^2.

1, 49, 169, 361, 625, 961, 1369, 1849, 2401, 3025, 3721, 4489, 5329, 6241, 7225, 8281, 9409, 10609, 11881, 13225, 14641, 16129, 17689, 19321, 21025, 22801, 24649, 26569, 28561, 30625, 32761, 34969, 37249, 39601, 42025, 44521, 47089, 49729, 52441, 55225

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Comments

Except for 2, exponents e such that x^e-x+1 is reducible.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A000290, A005449, A086727, A016778 (bisection), A016921.

Programs

Magma

[(6*n+1)^2: n in [0..60]]; // Vincenzo Librandi, May 04 2011

Maple

A016922:=n->(6*n+1)^2; seq(A016922(n), n=0..100); # Wesley Ivan Hurt, Dec 06 2013

Mathematica

Table[(6n+1)^2, {n,0,100}] (* or *)
CoefficientList[Series[(1 + 46*x + 25*x^2)/(1 - x)^3, {x, 0, 30}], x] (* Wesley Ivan Hurt, Oct 13 2014 *)
LinearRecurrence[{3,-3,1},{1,49,169},50] (* Harvey P. Dale, Feb 17 2023 *)

PARI

a(n)=(6*n+1)^2 \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f.: ( 1+46*x+25*x^2 ) / (1-x)^3. - R. J. Mathar, Mar 10 2011

a(n) = A016921(n)^2 = A000290(A016921(n)). - Wesley Ivan Hurt, Dec 06 2013

a(n) = 24*A005449(n)+1. - Jean-Bernard François, Oct 12 2014

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Wesley Ivan Hurt, Oct 13 2014

Sum_{n>=0} 1/a(n) = A086727. - Amiram Eldar, Nov 16 2020