NAME
a(n) = (n^2 - 3*n + 1 + (-1)^n)/2.
LINKS
G. C. Greubel, <a href="/A176222/b176222.txt">Table of n, a(n) for n = 3..1000</a>
FORMULA
a(n) = (n - t(n))*(n - 3 + t(n))/2, where t(n) = 1-(n mod 2).
G.f.: x^4*(-3+-x) / ( (1+x)*(x-1-x)^3 ). - R. J. Mathar, Mar 06 2011
From Bruno Berselli, Sep 13 2011: (Start)
a(n) + a(n+1) = A005563(n-2). a(-n) = A084265(n). - _Bruno Berselli_, Sep 13 2011
a(-n) = A084265(n). (End)
a(n) = 1 -2n2*n +floor(n/2) +floor(n^2/2). - Wesley Ivan Hurt, Jun 14 2013
E.g.f.: (1/2)*((1-x)*exp(x/2) - exp(-x/2))^2. - G. C. Greubel, Mar 22 2022
PROG
(Sage) [n*(n-3)/2 + ((n+1)%2) for n in (3..60)] # G. C. Greubel, Mar 22 2022
STATUS
approved
editing