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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.

%I A374394 #13 Jul 13 2024 11:10:22
%S A374394 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,
%T A374394 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,
%U A374394 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
%N 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.
%H A374394 Rémy Sigrist, <a href="/A374394/b374394.txt">Table of n, a(n) for n = 0..8190</a>
%H A374394 Rémy Sigrist, <a href="/A374394/a374394.gp.txt">PARI program</a>
%H A374394 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A374394 T(n, k) = A022290(A374354(1+A003754(n)), k).
%e A374394 Triangle T(n, k) begins:
%e A374394   n   n-th row
%e A374394   --  ------------------------
%e A374394    0  0
%e A374394    1  0, 1
%e A374394    2  0, 2
%e A374394    3  1, 2
%e A374394    4  0, 1, 3, 4
%e A374394    5  2, 3
%e A374394    6  2, 4
%e A374394    7  0, 2, 5, 7
%e A374394    8  1, 2, 6, 7
%e A374394    9  3, 4, 5, 6
%e A374394   10  3, 7
%e A374394   11  4, 7
%e A374394   12  0, 1, 3, 4, 8, 9, 11, 12
%e A374394   13  2, 3, 10, 11
%e A374394   14  2, 4, 10, 12
%o A374394 (PARI) \\ See Links section.
%Y A374394 Cf. A003754, A022290, A277561, A374354, A374395, A374396.
%K A374394 nonn,base,tabf
%O A374394 0,5
%A A374394 _Rémy Sigrist_, Jul 07 2024