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A146302 a(n) = (8*n+5)*(8*n+9). 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

f(y) = y^4*(1 + y^4) = y^4 - y^8 + y^12 - y^16 + y^20 - y^24 + ... int(f(y), y) = y^5/5 - y^9/9 + y^13/13 - y^17/17 + y^21/21 - y^25/25 + ... int(f(y), y=0..1) = 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 + ... int(f(y), y=0..1) = sum(4/(8*m+5)/(8*m+9), m=0..infinity) = = -1/8*sqrt(2)*Pi+1-1/4*sqrt(2)*log(1+sqrt(2)) = = 0.13302701266008896241... - Miklos Kristof, Nov 03 2008

LINKS

Table of n, a(n) for n=0..35.

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

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

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 *)

PROG

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

CROSSREFS

Sequence in context: A158634 A091197 A184539 * A203835 A087442 A280059

Adjacent sequences:  A146299 A146300 A146301 * A146303 A146304 A146305

KEYWORD

nonn,easy

AUTHOR

Miklos Kristof, Oct 29 2008

STATUS

approved

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Last modified August 16 11:10 EDT 2017. Contains 290623 sequences.