OFFSET
0,3
COMMENTS
Partial sums of A175885. - Reinhard Zumkeller, Jan 07 2012
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
FORMULA
a(n) = 11*n^2/4 + 7*((-1)^n - 1)/8.
a(n) = -a(n-1) + A069125(n). - Vincenzo Librandi, Sep 30 2011
From Colin Barker, Sep 15 2013: (Start)
a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
G.f.: -x*(x^2+9*x+1) / ((x-1)^3*(x+1)). (End)
Sum_{n>=1} 1/a(n) = Pi^2/66 + tan(sqrt(7/11)*Pi/2)*Pi/sqrt(77). - Amiram Eldar, Jan 16 2023
MATHEMATICA
LinearRecurrence[{2, 0, -2, 1}, {0, 1, 11, 23}, 50] (* Harvey P. Dale, May 20 2019 *)
PROG
(Magma) [11*n^2/4+7*((-1)^n-1)/8: n in [0..50]]; // Vincenzo Librandi, Sep 30 2011
(Haskell)
a195043 n = a195043_list !! n
a195043_list = scanl (+) 0 a175885_list
-- Reinhard Zumkeller, Jan 07 2012
(PARI) Vec(-x*(x^2+9*x+1)/((x-1)^3*(x+1)) + O(x^100)) \\ Colin Barker, Sep 15 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Omar E. Pol, Sep 27 2011
STATUS
approved