A374667 Triangle T(n,k) (1 <= k <= n) read by rows: T(n,k) = c_n * F(k)/F(k+2) where c_n = LCM of F(3), F(4), ... F(n+2) (and F() are the Fibonacci numbers).

1, 3, 2, 15, 10, 12, 60, 40, 48, 45, 780, 520, 624, 585, 600, 5460, 3640, 4368, 4095, 4200, 4160, 92820, 61880, 74256, 69615, 71400, 70720, 70980, 1021020, 680680, 816816, 765765, 785400, 777920, 780780, 779688, 90870780, 60580520, 72696624, 68153085, 69900600, 69234880, 69489420, 69392232, 69429360

Offset: 1

Author

J. Lowell, Jul 15 2024

Keywords

• nonn
• tabl

Examples

			Triangle begins:
      1;
      3,     2;
     15,    10,    12;
     60,    40,    48,    45;
    780,   520,   624,   585,   600;
   5460,  3640,  4368,  4095,  4200,  4160;
  92820, 61880, 74256, 69615, 71400, 70720, 70980;
  ...
Fifth row is 780, 520, 624, 585, 600. These are 1/2, 1/3, 2/5, 3/8, 5/13 of c_5 = 1560.
		

Crossrefs

Cf. A000045, A035105.

Programs

PARI

row(n)={my(m=lcm(vector(n,k,fibonacci(k+2)))); vector(n, k, fibonacci(k)*m/fibonacci(k+2))}

Formula

T(n,k) = A035105(n+2) * A000045(k) / A000045(k+2).