A154599 a(n) = 2*n^2 + 20*n + 8.

30, 56, 86, 120, 158, 200, 246, 296, 350, 408, 470, 536, 606, 680, 758, 840, 926, 1016, 1110, 1208, 1310, 1416, 1526, 1640, 1758, 1880, 2006, 2136, 2270, 2408, 2550, 2696, 2846, 3000, 3158, 3320, 3486, 3656, 3830, 4008, 4190, 4376, 4566, 4760, 4958, 5160

Offset: 1

Author

Vincenzo Librandi, Jan 12 2009

Keywords

• nonn
• easy

Comments

Tenth diagonal of A144562.

2*a(n) + 84 is a square.

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Crossrefs

Cf. A067076, A127147, A144562, A153238.

Programs

Magma

I:=[30, 56, 86]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 26 2012

Mathematica

LinearRecurrence[{3, -3, 1}, {30, 56, 86}, 50] (* Vincenzo Librandi, Feb 26 2012 *)
Table[2n^2+20n+8,{n,50}] (* Harvey P. Dale, Jun 15 2019 *)

PARI

for(n=1, 40, print1(2*n^2+20*n+8", ")); \\ Vincenzo Librandi, Feb 26 2012

SageMath

[2*n^2+20*n+8 for n in range(1,41)] # G. C. Greubel, May 30 2024

Formula

From R. J. Mathar, Jan 05 2011: (Start)

a(n) = 2*A127147(n+13).

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

From Amiram Eldar, Feb 25 2023: (Start)

Sum_{n>=1} 1/a(n) = 79/952 - cot(sqrt(21)*Pi)*Pi/(4*sqrt(21)).

Sum_{n>=1} (-1)^(n+1)/a(n) = 2851/14280 - cosec(sqrt(21)*Pi)*Pi/(4*sqrt(21)). (End)

E.g.f.: 2*(-4 + (4 + 11*x + x^2)*exp(x)). - G. C. Greubel, May 30 2024