OFFSET
0,1
LINKS
T. D. Noe, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = 162*n + a(n-1) with a(0)=8. - Vincenzo Librandi, Nov 12 2010
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
G.f.: -((2*(x*(4*x+73)+4))/(x-1)^3). - 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
From Amiram Eldar, Feb 19 2023: (Start)
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)
E.g.f.: exp(x)*(8 + 81*x*(2 + x)). - Elmo R. Oliveira, Oct 18 2024
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
(PARI) a(n)=(9*n+1)*(9*n+8) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved