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

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, 14, 58, 15, 31, 16, 66, 17, 35, 18, 74, 19, 39, 20, 82, 21, 43, 22, 90, 23, 47, 24, 98, 25, 51, 26

Offset: 0

Author

Paul Curtz, Apr 25 2010

Keywords

• nonn
• easy

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).

Crossrefs

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

Programs

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 *)

PARI

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

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