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

1,2

Links

Table of n, a(n) for n=1..45.

Formula

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

Example

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.

Prog

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

Crossrefs

Cf. A000045, A035105.

Sequence in context: A345291 A185973 A258566 * A051917 A302845 A291251

Adjacent sequences: A374664 A374665 A374666 * A374668 A374669 A374670

Keyword

nonn,tabl

Author

J. Lowell, Jul 15 2024

Status

approved