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%I #13 Mar 27 2023 03:42:47
%S 0,0,1,0,2,0,3,0,1,3,4,0,5,0,1,5,6,0,2,5,7,0,8,0,1,8,9,0,2,8,10,0,3,8,
%T 11,0,1,3,4,8,9,11,12,0,13,0,1,13,14,0,2,13,15,0,3,13,16,0,1,3,4,13,
%U 14,16,17,0,5,13,18,0,1,5,6,13,14,18,19,0,2,5,7,13,15,18,20
%N Irregular triangle T(n, k), n >= 0, k = 1..2^A007895(n), read by rows; the n-th row lists the numbers k such that the Fibonacci numbers that appear in the Zeckendorf representation of k also appear in that of n.
%C In other words, the n-th row lists the numbers k such that A003714(n) AND A003714(k) = A003714(k) (where AND denotes the bitwise AND operator).
%C The Zeckendorf representation is also known as the greedy Fibonacci representation (see A356771 for further details).
%H Rémy Sigrist, <a href="/A361755/b361755.txt">Table of n, a(n) for n = 0..10924</a> (rows for n = 0..610 flattened)
%H Rémy Sigrist, <a href="/A361755/a361755.gp.txt">PARI program</a>
%H <a href="/index/Z#Zeckendorf">Index entries for sequences related to Zeckendorf expansion of n</a>
%F T(n, 1) = 0.
%F T(n, 2) = A139764(n) for any n > 0.
%F T(n, 2^A007895(n)) = n.
%e Triangle T(n, k) begins:
%e n n-th row
%e -- ------------------------
%e 0 0
%e 1 0, 1
%e 2 0, 2
%e 3 0, 3
%e 4 0, 1, 3, 4
%e 5 0, 5
%e 6 0, 1, 5, 6
%e 7 0, 2, 5, 7
%e 8 0, 8
%e 9 0, 1, 8, 9
%e 10 0, 2, 8, 10
%e 11 0, 3, 8, 11
%e 12 0, 1, 3, 4, 8, 9, 11, 12
%o (PARI) See Links section.
%Y See A361756 for a similar sequence.
%Y Cf. A003714, A007895, A139764, A295989, A356771.
%K nonn,tabf,base
%O 0,5
%A _Rémy Sigrist_, Mar 23 2023