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 A176743 a(n) = GCD( A000217(n+1), A002378(n+2)). 3

%I

%S 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 14,58,15,31,16,66,17,35,18,74,19,39,20,82,21,43,22,90,23,47,24,98,25,

%U 51,26

%N a(n) = GCD( A000217(n+1), A002378(n+2)).

%C 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 <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 a(2n) = n+1, a(2n+1) = A123167(n+2).

%F a(n) = 2*a(n-4) - a(n-8).

%F 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 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 := proc(n)

%p if type(n,'even') then

%p n/2+1 ;

%p else

%p A123167((n-1)/2+2) ;

%p end if;

%p end proc: # _R. J. Mathar_, Jul 25 2013

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

%o (PARI) a(n)=(n+2)*gcd((n+1)/2, n+3) \\ _Charles R Greathouse IV_, Sep 02 2015

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

%K nonn,easy

%O 0,2

%A _Paul Curtz_, Apr 25 2010

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)