A154590 a(n) = 2*n^2 + 16*n + 6.

24, 46, 72, 102, 136, 174, 216, 262, 312, 366, 424, 486, 552, 622, 696, 774, 856, 942, 1032, 1126, 1224, 1326, 1432, 1542, 1656, 1774, 1896, 2022, 2152, 2286, 2424, 2566, 2712, 2862, 3016, 3174, 3336, 3502, 3672, 3846, 4024, 4206, 4392, 4582, 4776, 4974, 5176

Offset

1,1

Comments

Eighth diagonal of A144562.

2*a(n) + 52 is a square.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

Formula

a(n) = 2*A116711(n+3).

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

From Amiram Eldar, Mar 02 2023: (Start)

Sum_{n>=1} 1/a(n) = 35/468 - cot(sqrt(13)*Pi)*Pi/(4*sqrt(13)).

Sum_{n>=1} (-1)^(n+1)/a(n) = 121/468 + cosec(sqrt(13)*Pi)*Pi/(4*sqrt(13)). (End)

Mathematica

Table[2n^2+16n+6, {n, 50}] (* or *) LinearRecurrence[{3, -3, 1}, {24, 46, 72}, 50] (* Harvey P. Dale, Dec 27 2011 *)

Prog

(PARI) a(n)=2*n^2+16*n+6 \\ Charles R Greathouse IV, Jun 17 2017

Crossrefs

Cf. A144562, A067076, A116711, A153238.

Sequence in context: A217080 A226327 A063323 * A028992 A220515 A215148

Adjacent sequences: A154587 A154588 A154589 * A154591 A154592 A154593

Keyword

nonn,easy,less

Author

Vincenzo Librandi, Jan 12 2009

Extensions

Corrected (a(31) added) by Harvey P. Dale, Dec 27 2011

Status

approved