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A326819 Irregular triangle read by rows; for n >= 0, the n-th row corresponds to the elements of the set {(n-k) AND k, k = 0..n}, in ascending order (where AND denotes the bitwise AND operator).

%I A326819 #13 Oct 20 2019 15:10:37
%S A326819 0,0,0,1,0,0,1,2,0,2,0,1,3,0,0,1,2,4,0,2,4,0,1,3,4,5,0,4,0,1,2,5,6,0,
%T A326819 2,6,0,1,3,7,0,0,1,2,4,8,0,2,4,8,0,1,3,4,5,8,9,0,4,8,0,1,2,5,6,8,9,10,
%U A326819 0,2,6,8,10,0,1,3,7,8,9,11,0,8,0,1,2,4,9,10,12
%N A326819 Irregular triangle read by rows; for n >= 0, the n-th row corresponds to the elements of the set {(n-k) AND k, k = 0..n}, in ascending order (where AND denotes the bitwise AND operator).
%C A326819 For any n >= 0, the n-th row:
%C A326819 - has sum A328564(n),
%C A326819 - has apparently length A002487(n+1),
%C A326819 - has first element 0,
%C A326819 - has last element A104594(n).
%H A326819 Rémy Sigrist, <a href="/A326819/b326819.txt">Table of n, a(n) for n = 0..9851</a> (rows n = 0..512)
%e A326819 Table begins:
%e A326819     0;
%e A326819     0;
%e A326819     0, 1;
%e A326819     0;
%e A326819     0, 1, 2;
%e A326819     0, 2;
%e A326819     0, 1, 3;
%e A326819     0;
%e A326819     0, 1, 2, 4;
%e A326819     0, 2, 4;
%e A326819     0, 1, 3, 4, 5;
%e A326819     0, 4;
%e A326819     0, 1, 2, 5, 6;
%e A326819     0, 2, 6;
%e A326819     0, 1, 3, 7;
%e A326819     ...
%p A326819 T:= n-> sort([{seq(Bits[And](n-k, k), k=0..n)}[]])[]:
%p A326819 seq(T(n), n=0..30);  # _Alois P. Heinz_, Oct 20 2019
%o A326819 (PARI) row(n) = Set(apply(k -> bitand(n-k, k), [0..n]))
%Y A326819 Cf. A326820 (OR variant), A328568 (XOR variant).
%Y A326819 Cf. A002487, A104594, A328564.
%K A326819 nonn,tabf,look,base
%O A326819 0,8
%A A326819 _Rémy Sigrist_, Oct 20 2019