A083651 - OEIS

%I #12 Sep 20 2021 08:51:51

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

%C n = Sum(T(n,k)*2^k: 0<=k<=n);

%C T(n, A070939(n))=1 for n>0, T(n,k)=0 for k>A070939(n);

%C T(n,0)=A000035(n); T(n,n)=0;

%C A021913(0)=T(0,0), A021913(n)=T(n,1) for n>0.

%e The triangle starts

%e 0

%e 1 0

%e 0 1 0

%e 1 1 0 0

%e 0 0 1 0 0

%e 1 0 1 0 0 0

%e 0 1 1 0 0 0 0

%e 1 1 1 0 0 0 0 0

%e 0 0 0 1 0 0 0 0 0

%e 1 0 0 1 0 0 0 0 0 0

%e 0 1 0 1 0 0 0 0 0 0 0

%e 1 1 0 1 0 0 0 0 0 0 0 0

%e 0 0 1 1 0 0 0 0 0 0 0 0 0

%e 1 0 1 1 0 0 0 0 0 0 0 0 0 0

%e 0 1 1 1 0 0 0 0 0 0 0 0 0 0 0

%p A083651 := proc(n,k)

%p     floor(n/2^k) ;

%p     modp(%,2) ;

%p end proc:  # _R. J. Mathar_, Apr 21 2021

%t row[n_] := row[n] = PadRight[Reverse[IntegerDigits[n, 2]], n+1];

%t T[n_, k_] := row[n][[k+1]];

%t Table[T[n, k], {n, 0, 14}, {k, 0, n}] // Flatten

%Y Cf. A000035 (column k=0), A133872 (k=1), A131078 (k=2), A000120 (row sums).

%K nonn,tabl,easy

%O 0,1

%A _Reinhard Zumkeller_, May 01 2003