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

0,5

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

Formula

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

Example

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

Prog

(PARI) \\ See Links section.

Crossrefs

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

Sequence in context: A099505 A156837 A255935 * A129559 A129680 A118231

Adjacent sequences: A374391 A374392 A374393 * A374395 A374396 A374397

Keyword

nonn,base,tabf

Author

Rémy Sigrist, Jul 07 2024

Status

approved