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 A221920 a(n) = 3*n/gcd(3*n, n+3), n >= 3. 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 3,1 COMMENTS This is the third column sequence (m = 3) of the triangle A221918. 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). 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] EXAMPLE a(6) = numerator(18/9) = numerator(2) = 2 = 18/gcd(18,9) = 18/9 = 18/gcd(9,9) = 18/9. PROG (PARI) a(n)=3*n/gcd(3*n, n+3) \\ Charles R Greathouse IV, Apr 18 2013 CROSSREFS Cf. A221918, A000027 (m=1), A145979(m=2), A221921 (m=4), A222463 (m=5). Sequence in context: A039945 A227302 A201273 * A349663 A188549 A287357 Adjacent sequences: A221917 A221918 A221919 * A221921 A221922 A221923 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Feb 21 2013 STATUS approved

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Last modified March 30 13:38 EDT 2023. Contains 361621 sequences. (Running on oeis4.)