A374394 Irregular table T(n, k), n >= 0, 0 <= k < A277561(1+A003754(n)), read by rows; the n-th row lists the numbers z <= n such that the Zeckendorf representations of z and n-z have no common Fibonacci numbers and when combined together correspond to the lazy Fibonacci representation of n.

0, 0, 1, 0, 2, 1, 2, 0, 1, 3, 4, 2, 3, 2, 4, 0, 2, 5, 7, 1, 2, 6, 7, 3, 4, 5, 6, 3, 7, 4, 7, 0, 1, 3, 4, 8, 9, 11, 12, 2, 3, 10, 11, 2, 4, 10, 12, 5, 7, 8, 10, 6, 7, 9, 10, 5, 6, 11, 12, 7, 11, 7, 12, 0, 2, 5, 7, 13, 15, 18, 20, 1, 2, 6, 7, 14, 15, 19, 20, 3, 4, 5, 6, 16, 17, 18, 19

Offset: 0

Author

Rémy Sigrist, Jul 07 2024

Keywords

• nonn
• base
• tabf

Examples

			Triangle T(n, k) begins:
  n   n-th row
  --  ------------------------
   0  0
   1  0, 1
   2  0, 2
   3  1, 2
   4  0, 1, 3, 4
   5  2, 3
   6  2, 4
   7  0, 2, 5, 7
   8  1, 2, 6, 7
   9  3, 4, 5, 6
  10  3, 7
  11  4, 7
  12  0, 1, 3, 4, 8, 9, 11, 12
  13  2, 3, 10, 11
  14  2, 4, 10, 12
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..8190
• Rémy Sigrist, PARI program
• Index entries for sequences related to Zeckendorf expansion of n

Crossrefs

Cf. A003754, A022290, A277561, A374354, A374395, A374396.

Programs

PARI

\\ See Links section.

Formula

T(n, k) = A022290(A374354(1+A003754(n)), k).