|
|
A177073
|
|
a(n) = (9*n+4)*(9*n+5).
|
|
2
|
|
|
20, 182, 506, 992, 1640, 2450, 3422, 4556, 5852, 7310, 8930, 10712, 12656, 14762, 17030, 19460, 22052, 24806, 27722, 30800, 34040, 37442, 41006, 44732, 48620, 52670, 56882, 61256, 65792, 70490, 75350, 80372, 85556, 90902, 96410, 102080, 107912, 113906, 120062
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 162*n+a(n-1) with n>0, a(0)=20.
a(0)=20, a(1)=182, a(2)=506, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3).
G.f.: -2*(x*(10*x+61)+10)/(x-1)^3. (End)
Sum_{n>=0} 1/a(n) = tan(Pi/18)*Pi/9.
Product_{n>=0} (1 - 1/a(n)) = sec(Pi/18)*cos(sqrt(5)*Pi/18).
Product_{n>=0} (1 + 1/a(n)) = sec(Pi/18)*cosh(sqrt(3)*Pi/18). (End)
|
|
MATHEMATICA
|
f[n_] := Module[{c = 9n}, (c+4)(c+5)]; Array[f, 40, 0] (* or *) LinearRecurrence[{3, -3, 1}, {20, 182, 506}, 40] (* Harvey P. Dale, Jun 24 2011 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|