A221920 a(n) = 3*n/gcd(3*n, n+3), n >= 3.

3, 12, 15, 2, 21, 24, 9, 30, 33, 12, 39, 42, 5, 48, 51, 18, 57, 60, 21, 66, 69, 8, 75, 78, 27, 84, 87, 30, 93, 96, 11, 102, 105, 36, 111, 114, 39, 120, 123, 14, 129, 132, 45, 138, 141, 48, 147, 150, 17, 156, 159, 54, 165, 168, 57, 174, 177, 20, 183, 186, 63

Offset: 3

Author

Wolfdieter Lang, Feb 21 2013

Keywords

• nonn
• easy

Comments

This is the third column sequence (m = 3) of the triangle A221918.

Examples

			a(6) = numerator(18/9) = numerator(2) = 2 = 18/gcd(18,9) = 18/9 = 18/gcd(9,9) = 18/9.
		

Links

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

Crossrefs

Cf. A221918, A000027 (m=1), A145979(m=2), A221921 (m=4), A222463 (m=5).

Programs

Mathematica

a[n_] := 3*n/GCD[3*n, n+3]; Array[a, 63, 3] (* Amiram Eldar, Oct 09 2023 *)

PARI

a(n)=3*n/gcd(3*n,n+3) \\ Charles R Greathouse IV, Apr 18 2013

Formula

a(n) = A221918(n,3) = numerator(n*3/(n+3)), n >= 3.

a(n) = 3*n/gcd(3*n,n+3), n >= 3.

a(n) = 3*n/gcd(9,n+3), n >= 3, (because gcd(n+3,3*n) = gcd(n+3,3*n - 3*(n+3)) = gcd(n+3,-3^2) = gcd(n+3,9)).

G.f.: -x^3*(6*x^17 + 3*x^16 - 3*x^14 - 6*x^13 - x^12 - 12*x^11 - 15*x^10 - 6*x^9 - 33*x^8 - 30*x^7 - 9*x^6 - 24*x^5 - 21*x^4 - 2*x^3 - 15*x^2 - 12*x - 3) / ((x-1)^2*(x^2 + x + 1)^2*(x^6 + x^3 + 1)^2). - Colin Barker, Feb 25 2013

Sum_{k=3..n} a(k) ~ (61/54) * n^2. - Amiram Eldar, Oct 09 2023