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

1,1

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).

Formula

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

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

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

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 *)

Prog

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

Crossrefs

Cf. A144562, A153238, A067076, A127147.

Sequence in context: A027578 A189712 A029713 * A048451 A154796 A350316

Adjacent sequences: A154596 A154597 A154598 * A154600 A154601 A154602

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 12 2009

Status

approved