A356326 The terms in the negaFibonacci representation of a(n) are the terms in common in the negaFibonacci representations of n and -n.

0, 0, 0, 0, -1, 0, 0, 0, 0, -1, -3, -3, -1, 0, 0, 0, 0, 4, 0, 0, 0, 0, -1, -3, -3, -1, -8, -8, -8, -8, -1, -3, -3, -1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 12, 10, 10, 12, 0, 0, 0, 0, 4, 0, 0, 0, 0, -1, -3, -3, -1, -8, -8, -8, -8, -1, -3, -3, -1, -21, -21, -21, -21, -17

Offset: 0

Author

Rémy Sigrist, Aug 03 2022

Keywords

• sign
• base

Examples

			For n = 11:
- using F(-k) = A039834(k):
- 11 = F(-1) + F(-4) + F(-7),
- -11 = F(-4) + F(-6),
- so a(11) = F(-4) = -3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10946
• Rémy Sigrist, PARI program
• Wikipedia, NegaFibonacci coding
• Index entries for sequences related to Zeckendorf expansion of n

Crossrefs

Cf. A000045, A039834, A062877, A215024, A215025, A356325, A356327.

Programs

PARI

See Links section.

Formula

a(n) = 0 iff n belongs to A062877.

a(n) = A356327(A215024(n) AND A215025(n)) (where AND denotes the bitwise AND operator).

Empirically:

- a(A000045(k)+m) = a(A000045(k+1)-m) for k >= 0, m = 0..A000045(k+1)-A000045(k).