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%I A334348 #15 Aug 03 2022 17:42:01
%S A334348 0,0,0,0,1,0,0,0,0,0,0,0,2,0,0,0,1,0,0,1,0,0,0,0,3,0,0,0,0,1,0,3,3,0,
%T A334348 1,0,0,0,0,0,4,0,0,0,0,0,0,2,0,0,0,0,2,0,0,0,1,0,0,1,5,1,0,0,1,0,0,0,
%U A334348 0,0,0,5,5,0,0,0,0,0,0,0,2,0,0,5,6,5,0
%N A334348 The terms in the Zeckendorf representation of T(n, k) correspond to the terms in common in the Zeckendorf representations of n and of k; square array T(n, k) read by antidiagonals, n, k >= 0.
%C A334348 This array has connections with the bitwise AND operator (A004198).
%H A334348 Rémy Sigrist, <a href="/A334348/b334348.txt">Table of n, a(n) for n = 0..11475</a> (antidiagonals 0..150)
%H A334348 Rémy Sigrist, <a href="/A334348/a334348.png">Colored representation of (x, y) for 0 <= x, y <= 1000</a> (where the hue is function of T(x, y))
%H A334348 Rémy Sigrist, <a href="/A334348/a334348.gp.txt">PARI program for A334348</a>
%H A334348 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zeckendorf&#39;s_theorem">Zeckendorf's theorem</a>
%H A334348 <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F A334348 T(n, k) = A022290(A003714(n) AND A003714(k)) (where AND denotes the bitwise AND operator, A004198).
%F A334348 T(n, 0) = 0.
%F A334348 T(n, n) = n.
%F A334348 T(n, k) = T(k, n).
%F A334348 T(m, T(n, k)) = T(T(m, n), k).
%e A334348 Square array begins:
%e A334348   n\k|  0  1  2  3  4  5  6  7  8  9  10  11  12  13
%e A334348   ---+----------------------------------------------
%e A334348     0|  0  0  0  0  0  0  0  0  0  0   0   0   0   0
%e A334348     1|  0  1  0  0  1  0  1  0  0  1   0   0   1   0
%e A334348     2|  0  0  2  0  0  0  0  2  0  0   2   0   0   0
%e A334348     3|  0  0  0  3  3  0  0  0  0  0   0   3   3   0
%e A334348     4|  0  1  0  3  4  0  1  0  0  1   0   3   4   0
%e A334348     5|  0  0  0  0  0  5  5  5  0  0   0   0   0   0
%e A334348     6|  0  1  0  0  1  5  6  5  0  1   0   0   1   0
%e A334348     7|  0  0  2  0  0  5  5  7  0  0   2   0   0   0
%e A334348     8|  0  0  0  0  0  0  0  0  8  8   8   8   8   0
%e A334348     9|  0  1  0  0  1  0  1  0  8  9   8   8   9   0
%e A334348    10|  0  0  2  0  0  0  0  2  8  8  10   8   8   0
%e A334348    11|  0  0  0  3  3  0  0  0  8  8   8  11  11   0
%e A334348    12|  0  1  0  3  4  0  1  0  8  9   8  11  12   0
%e A334348    13|  0  0  0  0  0  0  0  0  0  0   0   0   0  13
%o A334348 (PARI) See Links section.
%Y A334348 Cf. A003714, A022290, A004198, A332022, A332565.
%K A334348 nonn,tabl,look,base
%O A334348 0,13
%A A334348 _Rémy Sigrist_, Apr 24 2020

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