|
|
A001534
|
|
a(n) = (9*n+1)*(9*n+8).
|
|
1
|
|
|
8, 170, 494, 980, 1628, 2438, 3410, 4544, 5840, 7298, 8918, 10700, 12644, 14750, 17018, 19448, 22040, 24794, 27710, 30788, 34028, 37430, 40994, 44720, 48608, 52658, 56870, 61244, 65780, 70478, 75338, 80360, 85544, 90890, 96398, 102068, 107900, 113894, 120050
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) with a(0)=8, a(1)=170, a(2)=494. - Harvey P. Dale, Aug 20 2011
Sum_{n>=0} 1/a(n) = (Psi(8/9)-Psi(1/9))/63 = 0.13700722.. - R. J. Mathar, May 30 2022
Sum_{n>=0} 1/a(n) = cot(Pi/9)*Pi/63. - Amiram Eldar, Sep 10 2022
Product_{n>=0} (1 - 1/a(n)) = cosec(Pi/9)*cos(sqrt(53)*Pi/18).
Product_{n>=0} (1 + 1/a(n)) = cosec(Pi/9)*cos(sqrt(5)*Pi/6). (End)
|
|
MATHEMATICA
|
f[n_]:=Module[{n9=9n}, (n9+1)(n9+8)]; Array[f, 40, 0] (* or *) LinearRecurrence[ {3, -3, 1}, {8, 170, 494}, 50] (* Harvey P. Dale, Aug 20 2011 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|