A146302 a(n) = (8*n+5)*(8*n+9).

45, 221, 525, 957, 1517, 2205, 3021, 3965, 5037, 6237, 7565, 9021, 10605, 12317, 14157, 16125, 18221, 20445, 22797, 25277, 27885, 30621, 33485, 36477, 39597, 42845, 46221, 49725, 53357, 57117, 61005, 65021, 69165, 73437, 77837, 82365

Offset: 0

Author

Miklos Kristof, Oct 29 2008

Keywords

• nonn
• easy

Comments

From Miklos Kristof, Nov 03 2008: (Start)

f(y) = y^4*(1 + y^4) = y^4 - y^8 + y^12 - y^16 + y^20 - y^24 + ...

Integral_{y} f(y) dy = y^5/5 - y^9/9 + y^13/13 - y^17/17 + y^21/21 - y^25/25 + ...

Integral_{y=0..1} f(y) dy = 1/5 - 1/9 + 1/13 - 1/17 + 1/21 - 1/25 + ...

= (9 - 5)/(5*9) + (17 - 13)/(13*17) + (25 - 21)/(21*25) + ...

= 4/(5*9) + 4/(13*17) + 4/(21*25) + ...

Integral_{y=0..1} f(y) dy = Sum_{m>=0} 4/((8*m+5)*(8*m+9))

= -(1/8)*sqrt(2)*Pi + 1 - (1/4)*sqrt(2)*log(1+sqrt(2))

= 0.13302701266008896241... (End)

Links

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

Programs

Maple

seq((8*m+5)*(8*m+9),m=0..40); # Miklos Kristof, Nov 03 2008

Mathematica

Table[(8n+5)(8n+9),{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{45,221,525},40] (* Harvey P. Dale, Oct 10 2015 *)

PARI

a(n)=(8*n+5)*(8*n+9) \\ Charles R Greathouse IV, Jun 17 2017

Formula

G.f: (45 + 86*x - 3*x^2)/(1-x)^3.

E.g.f.: (45 + 176*x + 64*x^2)*exp(x).

a(n) = A004770(n) * A004768(n). - Reinhard Zumkeller, Oct 30 2008