A145923 Second bisection of A061041: a(n) = A061041(2n+1) = (2*n+1)*(2*n+9).

9, 33, 65, 105, 153, 209, 273, 345, 425, 513, 609, 713, 825, 945, 1073, 1209, 1353, 1505, 1665, 1833, 2009, 2193, 2385, 2585, 2793, 3009, 3233, 3465, 3705, 3953, 4209, 4473, 4745, 5025, 5313, 5609, 5913, 6225, 6545, 6873, 7209, 7553, 7905, 8265, 8633, 9009, 9393

Offset: 0

Author

Paul Curtz, Oct 25 2008

Keywords

• nonn
• easy
• less

Links

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

Crossrefs

Cf. A061041.

Programs

Magma

[(2*n+5)^2-16: n in [0..60]]; // G. C. Greubel, Mar 23 2024

Mathematica

A145923[n_]:=4n^2+20n+9; Array[A145923,100,0] (* or *)
LinearRecurrence[{3,-3,1},{9,33,65},100] (* Paolo Xausa, Dec 05 2023 *)
(2*Range[0,60] +5)^2 -16 (* G. C. Greubel, Mar 23 2024 *)

PARI

a(n)=4*n^2+20*n+9 \\ Charles R Greathouse IV, Jun 17 2017

SageMath

[(2*n+5)^2-16 for n in range(61)] # G. C. Greubel, Mar 23 2024

Formula

a(n) = (2*n+1)*(2*n+9).

G.f.: (9 + 6*x - 7*x^2)/(1-x)^3 . - R. J. Mathar, Oct 23 2016

E.g.f.: (9 + 24*x + 4*x^2)*exp(x). - G. C. Greubel, Mar 23 2024

Extensions

More terms from Jinyuan Wang, Mar 23 2020