A356325 Array A(n, k), n, k >= 0, read by antidiagonals; the terms in the negaFibonacci representation of A(n, k) are the terms in common in the negaFibonacci representations of n and k.

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 1, 0, 0, 0, 2, 2, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 2, 1, 5, 5, 1, 2, 1, 0, 0, 0, 2, 2, 5, 5, 5, 2, 2, 0, 0, 0, 0, 0, 3, 5, 5, 5, 5, 3, 0, 0, 0, 0, 1, 0, 0, 5, 5, 6, 5, 5, 0, 0, 1, 0

Offset: 0

Author

Rémy Sigrist, Aug 03 2022

Keywords

• nonn
• base
• tabl

Comments

This sequence has similarities with A334348.

Examples

			Array A(n, k) begins:
  n\k|  0  1  2  3   4  5  6  7  8   9  10  11  12  13
  ---+------------------------------------------------
    0|  0  0  0  0   0  0  0  0  0   0   0   0   0   0
    1|  0  1  0  1   0  0  1  0  1   0   0   1   0   0
    2|  0  0  2  2   0  0  0  2  2   0   0   0   0   0
    3|  0  1  2  3   0  0  1  2  3   0   0   1   0   0
    4|  0  0  0  0   4  5  5  5  5  -1   0   0  -1   0
    5|  0  0  0  0   5  5  5  5  5   0   0   0   0   0
    6|  0  1  0  1   5  5  6  5  6   0   0   1   0   0
    7|  0  0  2  2   5  5  5  7  7   0   0   0   0   0
    8|  0  1  2  3   5  5  6  7  8   0   0   1   0   0
    9|  0  0  0  0  -1  0  0  0  0   9  10  10  12  13
   10|  0  0  0  0   0  0  0  0  0  10  10  10  13  13
   11|  0  1  0  1   0  0  1  0  1  10  10  11  13  13
   12|  0  0  0  0  -1  0  0  0  0  12  13  13  12  13
   13|  0  0  0  0   0  0  0  0  0  13  13  13  13  13
.
For n = 14 and k = 43:
- using F(-k) = A039834(k):
- 14 = F(-1) + F(-7),
- 43 = F(-2) + F(-4) + F(-7) + F(-9),
- so A(14, 43) = F(-7) = 13.
		

Links

• Rémy Sigrist, Colored representation of the array for n, k <= 1000 (white for 0's, shades of blue for negative values, shades of red for positive values)
• Rémy Sigrist, PARI program
• Wikipedia, NegaFibonacci coding
• Index entries for sequences related to Zeckendorf expansion of n

Crossrefs

Cf. A004198, A039834, A215024, A309076, A334348, A356326, A356327.

Programs

PARI

See Links section.

Formula

A(n, k) = A(k, n).

A(n, n) = n.

A(n, 0) = 0.

A(n, k) = A356327(A215024(n) AND A215024(k)) (where AND denotes the bitwise AND operator).