login
A166525
a(n) = 10*n - a(n-1), with n>1, a(1)=1.
10
1, 19, 11, 29, 21, 39, 31, 49, 41, 59, 51, 69, 61, 79, 71, 89, 81, 99, 91, 109, 101, 119, 111, 129, 121, 139, 131, 149, 141, 159, 151, 169, 161, 179, 171, 189, 181, 199, 191, 209, 201, 219, 211, 229, 221, 239, 231, 249, 241, 259, 251, 269, 261, 279, 271, 289
OFFSET
1,2
FORMULA
G.f.: x*(1+18*x-9*x^2) / ( (1+x)*(1-x)^2 ). - R. J. Mathar, Mar 08 2011
From G. C. Greubel, May 16 2016: (Start)
E.g.f.: (1/2)*(13*exp(-x) + 5*(1 + 2*x)*exp(x) - 18).
a(n) = a(n-1) + a(n-2) - a(n-3). (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = 1/9 + sqrt(5+2*sqrt(5))*Pi/10. - Amiram Eldar, Feb 24 2023
a(n) = (1/2)*(10*n + 5 + 13*(-1)^n). - G. C. Greubel, Aug 04 2024
MATHEMATICA
CoefficientList[Series[(1 +18 x -9 x^2)/((1+x) (1-x)^2), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{1, 1, -1}, {1, 19, 11}, 50] (* G. C. Greubel, May 16 2016 *)
PROG
(Magma) [n eq 1 select 1 else 10*n-Self(n-1): n in [1..80]]; // Vincenzo Librandi, Sep 13 2013
(SageMath)
def A166525(n): return 5*n - 4 + 13*((n+1)%2)
[A166525(n) for n in range(1, 101)] # G. C. Greubel, Aug 04 2024
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Oct 16 2009
STATUS
approved