A155966 a(n) = 2*n^2 + 8.

8, 10, 16, 26, 40, 58, 80, 106, 136, 170, 208, 250, 296, 346, 400, 458, 520, 586, 656, 730, 808, 890, 976, 1066, 1160, 1258, 1360, 1466, 1576, 1690, 1808, 1930, 2056, 2186, 2320, 2458, 2600, 2746, 2896, 3050, 3208, 3370, 3536, 3706, 3880, 4058, 4240, 4426, 4616

Offset: 0

Author

Vincenzo Librandi, Jan 31 2009

Keywords

• nonn
• easy

Comments

The identity (n^3 + 4*n)^2 + (2*n^2 + 8)^2 = (n^2 + 4)^3 can be written as A155965(n)^2 + a(n)^2 = A087475(n)^3.

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. A087475, A155965.

Cf. similar sequences listed in A255843.

Programs

Magma

[2*n^2+8: n in [0..50]]; // Vincenzo Librandi, Feb 22 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {8, 10, 16}, 50] (* Vincenzo Librandi, Feb 22 2012 *)
2*Range[0,50]^2+8 (* Harvey P. Dale, Mar 01 2018 *)

PARI

a(n)=2*n^2+8 \\ Charles R Greathouse IV, Jan 11 2012

Formula

G.f.: 2*(4 - 7*x + 5*x^2)/(1 - x)^3.

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

a(n) = 2*A087475(n). - Bruno Berselli, Mar 13 2015

From Amiram Eldar, Feb 25 2023: (Start)

Sum_{n>=0} 1/a(n) = 1/16 + coth(2*Pi)*Pi/8.

Sum_{n>=0} (-1)^n/a(n) = 1/16 + cosech(2*Pi)*Pi/8. (End)

E.g.f.: 2*exp(x)*(4 + x + x^2). - Elmo R. Oliveira, Jan 17 2025

Extensions

Offset changed from 1 to 0 and added a(0)=8 by Bruno Berselli, Mar 13 2015