cp's OEIS Frontend

A176743 a(n) = gcd(A000217(n+1), A002378(n+2)).

%I A176743 #27 Aug 02 2019 22:44:21
%S A176743 1,3,2,10,3,7,4,18,5,11,6,26,7,15,8,34,9,19,10,42,11,23,12,50,13,27,
%T A176743 14,58,15,31,16,66,17,35,18,74,19,39,20,82,21,43,22,90,23,47,24,98,25,
%U A176743 51,26
%N A176743 a(n) = gcd(A000217(n+1), A002378(n+2)).
%C A176743 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.
%H A176743 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F A176743 a(2n) = n+1, a(2n+1) = A123167(n+2).
%F A176743 a(n) = 2*a(n-4) - a(n-8).
%F A176743 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
%F A176743 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
%p A176743 A176743 := proc(n)
%p A176743     if type(n,'even') then
%p A176743         n/2+1 ;
%p A176743     else
%p A176743         A123167((n-1)/2+2) ;
%p A176743     end if;
%p A176743 end proc: # _R. J. Mathar_, Jul 25 2013
%t A176743 Table[GCD[Plus@@Range[n + 1], (n + 2)(n + 3)], {n, 0, 49}] (* _Alonso del Arte_, Jan 16 2011 *)
%o A176743 (PARI) a(n)=(n+2)*gcd((n+1)/2, n+3) \\ _Charles R Greathouse IV_, Sep 02 2015
%Y A176743 Cf. A000217 (triangular), A002378 (oblong), A176662.
%K A176743 nonn,easy
%O A176743 0,2
%A A176743 _Paul Curtz_, Apr 25 2010