OFFSET
0,2
COMMENTS
These greatest common divisors of (n+1)*(n+2)/2 and (n+2)*(n+3) appear in the second row of the table discussed in A177427: 0, -1/6, -1/4, -3/10, -1/3, -5/14, -3/8, -7/18, -2/5, ... These fractions can be written as A000217(n+1)/A002378(n+2), n >= 0, and the current sequence shows the common factors that reduces the fractions to the standard format with coprime numerator and denominator.
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).
FORMULA
a(2n) = n+1, a(2n+1) = A123167(n+2).
a(n) = 2*a(n-4) - a(n-8).
G.f.: (1 + 3*x + 2*x^2 + 10*x^3 + x^4 + x^5 - 2*x^7) / ( (x-1)^2*(1+x)^2*(x^2+1)^2 ). - R. J. Mathar, Jan 16 2011
a(n) = (8*n + 16 - 4*(n+2)*(-1)^n + (2*n + 5 + (-1)^n)*((1-(-1)^n)*(-1)^((2*n + 3 + (-1)^n)/4)))/8. - Luce ETIENNE, Feb 03 2015
MAPLE
A176743 := proc(n)
if type(n, 'even') then
n/2+1 ;
else
A123167((n-1)/2+2) ;
end if;
end proc: # R. J. Mathar, Jul 25 2013
MATHEMATICA
Table[GCD[Plus@@Range[n + 1], (n + 2)(n + 3)], {n, 0, 49}] (* Alonso del Arte, Jan 16 2011 *)
PROG
(PARI) a(n)=(n+2)*gcd((n+1)/2, n+3) \\ Charles R Greathouse IV, Sep 02 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Paul Curtz, Apr 25 2010
STATUS
approved