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%I #17 Aug 13 2021 19:49:49
%S 0,1,2,3,4,5,6,7,8,9,10,12,11,13,14,15,16,17,18,20,24,19,21,22,25,26,
%T 28,23,27,29,30,31,32,33,34,36,40,48,35,37,38,41,42,44,49,50,52,56,39,
%U 43,45,46,51,53,54,57,58,60,47,55,59,61,62,63,64,65,66
%N Triangle read by rows: equivalence classes of natural numbers, where numbers are equivalent when having equal numbers of zeros and ones in binary representation, respectively.
%C Row lengths are given by Pascal's triangle (cf. A007318), seen as flattened sequence, or for n > 0: length of n-th row = A007318(A003056(n-1),A002262(n-1));
%C 1 <= i < j <= length of n-th row: A023416(T(n,i)) = A023416(T(n,j)), A000120(T(n,i)) = A000120(T(n,j)) and A070939(T(n,i)) = A070939(T(n,j));
%C the table provides a permutation of the natural numbers when seen as flattened sequence.
%H Reinhard Zumkeller, <a href="/A187769/b187769.txt">Rows n = 0..78 of triangle, flattened - all terms < 2^12</a>
%H Reinhard Zumkeller, <a href="/A187769/a187769.txt">Illustration of initial terms</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the nonnegative integers</a>
%e See link.
%o (Haskell)
%o import List (elemIndices)
%o a187769 n k = a187769_tabf !! n !! k
%o a187769_row n = a187769_tabf !! n
%o a187769_tabf = [0] : [elemIndices (b, len - b) $
%o takeWhile ((<= len) . uncurry (+)) $ zip a000120_list a023416_list |
%o len <- [1 ..], b <- [1 .. len]]
%o a187769_list = concat a187769_tabf
%Y Rows of A187786, duplicates removed;
%Y Cf. A099627 (left edge), A023758 (right edge).
%Y Cf. A294648.
%K nonn,base,tabf
%O 0,3
%A _Reinhard Zumkeller_, Jan 05 2013
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