0,2

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.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,2,0,0,0,-1).

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

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

Table[GCD[Plus@@Range[n + 1], (n + 2)(n + 3)], {n, 0, 49}] (* Alonso del Arte, Jan 16 2011 *)

(PARI) a(n)=(n+2)*gcd((n+1)/2, n+3) \\ Charles R Greathouse IV, Sep 02 2015

Cf. A000217 (triangular), A002378 (oblong), A176662.

Sequence in context: A354191 A135515 A114486 * A220466 A090780 A184174

Adjacent sequences: A176740 A176741 A176742 * A176744 A176745 A176746

nonn,easy

Paul Curtz, Apr 25 2010

approved