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A083651 Triangular array, read by rows: T(n,k) = k-th bit in binary representation of n (0<=k<=n).

%I A083651 #12 Sep 20 2021 08:51:51
%S A083651 0,1,0,0,1,0,1,1,0,0,0,0,1,0,0,1,0,1,0,0,0,0,1,1,0,0,0,0,1,1,1,0,0,0,
%T A083651 0,0,0,0,0,1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,0,0,1,0,1,0,0,0,0,0,0,0,1,1,
%U A083651 0,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,1,0,1,1,0,0,0,0,0,0,0,0,0,0
%N A083651 Triangular array, read by rows: T(n,k) = k-th bit in binary representation of n (0<=k<=n).
%C A083651 n = Sum(T(n,k)*2^k: 0<=k<=n);
%C A083651 T(n, A070939(n))=1 for n>0, T(n,k)=0 for k>A070939(n);
%C A083651 T(n,0)=A000035(n); T(n,n)=0;
%C A083651 A021913(0)=T(0,0), A021913(n)=T(n,1) for n>0.
%e A083651 The triangle starts
%e A083651 0
%e A083651 1 0
%e A083651 0 1 0
%e A083651 1 1 0 0
%e A083651 0 0 1 0 0
%e A083651 1 0 1 0 0 0
%e A083651 0 1 1 0 0 0 0
%e A083651 1 1 1 0 0 0 0 0
%e A083651 0 0 0 1 0 0 0 0 0
%e A083651 1 0 0 1 0 0 0 0 0 0
%e A083651 0 1 0 1 0 0 0 0 0 0 0
%e A083651 1 1 0 1 0 0 0 0 0 0 0 0
%e A083651 0 0 1 1 0 0 0 0 0 0 0 0 0
%e A083651 1 0 1 1 0 0 0 0 0 0 0 0 0 0
%e A083651 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0
%p A083651 A083651 := proc(n,k)
%p A083651     floor(n/2^k) ;
%p A083651     modp(%,2) ;
%p A083651 end proc:  # _R. J. Mathar_, Apr 21 2021
%t A083651 row[n_] := row[n] = PadRight[Reverse[IntegerDigits[n, 2]], n+1];
%t A083651 T[n_, k_] := row[n][[k+1]];
%t A083651 Table[T[n, k], {n, 0, 14}, {k, 0, n}] // Flatten
%Y A083651 Cf. A000035 (column k=0), A133872 (k=1), A131078 (k=2), A000120 (row sums).
%K A083651 nonn,tabl,easy
%O A083651 0,1
%A A083651 _Reinhard Zumkeller_, May 01 2003