A146301 a(n) = (8*n+3)*(8*n+7).

21, 165, 437, 837, 1365, 2021, 2805, 3717, 4757, 5925, 7221, 8645, 10197, 11877, 13685, 15621, 17685, 19877, 22197, 24645, 27221, 29925, 32757, 35717, 38805, 42021, 45365, 48837, 52437, 56165, 60021, 64005, 68117, 72357, 76725, 81221

Offset: 0

Author

Miklos Kristof, Oct 29 2008

Keywords

• nonn
• easy

Comments

Sum_{n>=0} 1/((8*n+3)*(8*n+7)) = (1/16)*sqrt(2)*(log(sqrt(2)-1) + Pi/2) = 0.60936936799920131042...

Links

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

Programs

Maple

seq((8*n+3)*(8*n+7),n=0..40);

Mathematica

Table[(8n+3)(8n+7),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{21,165,437},40] (* Harvey P. Dale, Aug 16 2015 *)

PARI

a(n)=(8*n+3)*(8*n+7) \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f: (21 + 102*x + 5*x^2)/(1-x)^3.

E.g.f.: (21 + 144*x + 64*x^2)*exp(x).