OFFSET
1,1
LINKS
FORMULA
a(n) = 8*n - a(n-1) - 5 (with a(1)=4). - Vincenzo Librandi, Aug 06 2010
a(n) = 4*n -(1 + (-1)^n)/2. - Arkadiusz Wesolowski, Sep 18 2012
G.f.: x*(4+3*x+x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 10 2015
From Franck Maminirina Ramaharo, Jul 22 2018: (Start)
a(n) = A047470(n) + 4.
E.g.f.: (2 - exp(-x) + (8*x - 1)*exp(x))/2. (End)
Sum_{n>=1} (-1)^(n+1)/a(n) = (sqrt(2)+1)*Pi/16 - log(2)/4 - sqrt(2)*log(sqrt(2)+1)/8. - Amiram Eldar, Dec 11 2021
MAPLE
MATHEMATICA
Table[4n - (1 + (-1)^n)/2, {n, 100}] (* Wesley Ivan Hurt, Feb 24 2014 *)
PROG
(Maxima) makelist(4*n - (1 + (-1)^n)/2, n, 1, 100); /* Franck Maminirina Ramaharo, Jul 22 2018 */
(Python)
def A047535(n): return (n<<2)-(n&1^1) # Chai Wah Wu, Mar 30 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved