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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.

%I A356325 #10 Aug 05 2022 10:50:55
%S A356325 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,
%T A356325 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,
%U A356325 0,3,5,5,5,5,3,0,0,0,0,1,0,0,5,5,6,5,5,0,0,1,0
%N 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.
%C A356325 This sequence has similarities with A334348.
%H A356325 Rémy Sigrist, <a href="/A356325/a356325.png">Colored representation of the array for n, k <= 1000</a> (white for 0's, shades of blue for negative values, shades of red for positive values)
%H A356325 Rémy Sigrist, <a href="/A356325/a356325.gp.txt">PARI program</a>
%H A356325 Wikipedia, <a href="https://en.wikipedia.org/wiki/NegaFibonacci_coding">NegaFibonacci coding</a>
%H A356325 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A356325 A(n, k) = A(k, n).
%F A356325 A(n, n) = n.
%F A356325 A(n, 0) = 0.
%F A356325 A(n, k) = A356327(A215024(n) AND A215024(k)) (where AND denotes the bitwise AND operator).
%e A356325 Array A(n, k) begins:
%e A356325   n\k|  0  1  2  3   4  5  6  7  8   9  10  11  12  13
%e A356325   ---+------------------------------------------------
%e A356325     0|  0  0  0  0   0  0  0  0  0   0   0   0   0   0
%e A356325     1|  0  1  0  1   0  0  1  0  1   0   0   1   0   0
%e A356325     2|  0  0  2  2   0  0  0  2  2   0   0   0   0   0
%e A356325     3|  0  1  2  3   0  0  1  2  3   0   0   1   0   0
%e A356325     4|  0  0  0  0   4  5  5  5  5  -1   0   0  -1   0
%e A356325     5|  0  0  0  0   5  5  5  5  5   0   0   0   0   0
%e A356325     6|  0  1  0  1   5  5  6  5  6   0   0   1   0   0
%e A356325     7|  0  0  2  2   5  5  5  7  7   0   0   0   0   0
%e A356325     8|  0  1  2  3   5  5  6  7  8   0   0   1   0   0
%e A356325     9|  0  0  0  0  -1  0  0  0  0   9  10  10  12  13
%e A356325    10|  0  0  0  0   0  0  0  0  0  10  10  10  13  13
%e A356325    11|  0  1  0  1   0  0  1  0  1  10  10  11  13  13
%e A356325    12|  0  0  0  0  -1  0  0  0  0  12  13  13  12  13
%e A356325    13|  0  0  0  0   0  0  0  0  0  13  13  13  13  13
%e A356325 .
%e A356325 For n = 14 and k = 43:
%e A356325 - using F(-k) = A039834(k):
%e A356325 - 14 = F(-1) + F(-7),
%e A356325 - 43 = F(-2) + F(-4) + F(-7) + F(-9),
%e A356325 - so A(14, 43) = F(-7) = 13.
%o A356325 (PARI) See Links section.
%Y A356325 Cf. A004198, A039834, A215024, A309076, A334348, A356326, A356327.
%K A356325 nonn,base,tabl
%O A356325 0,13
%A A356325 _Rémy Sigrist_, Aug 03 2022