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A206566 Triangular array: T(i,j) = number of terms common to the binary expansions of i+1 and j, for j=1,2,3,...,i; i=1,2,3,...

%I A206566 #7 Jul 12 2012 00:40:00
%S A206566 0,1,1,0,0,0,1,0,1,1,0,1,1,1,1,1,1,2,1,2,2,0,0,0,0,0,0,0,1,0,1,0,1,0,
%T A206566 1,1,0,1,1,0,0,1,1,1,1,1,1,2,0,1,1,2,1,2,2,0,0,0,1,1,1,1,1,1,1,1,1,0,
%U A206566 1,1,2,1,2,1,2,1,2,2,0,1,1,1,1,2,2,1,1,2,2,2,2,1,1,2,1,2,2,3,1
%N A206566 Triangular array:  T(i,j) = number of terms common to the binary expansions of i+1 and j, for j=1,2,3,...,i; i=1,2,3,...
%C A206566 Row n consists of the first n terms of column n+1 of A206479, and (n-th row sum)=A115478(n+1).
%e A206566 First ten rows:
%e A206566 0
%e A206566 1 1
%e A206566 0 0 0
%e A206566 1 0 1 1
%e A206566 0 1 1 1 1
%e A206566 1 1 2 1 2 2
%e A206566 0 0 0 0 0 0 0
%e A206566 1 0 1 0 1 0 1 1
%e A206566 0 1 1 0 0 1 1 1 1
%e A206566 1 1 2 0 1 1 2 1 2 2
%t A206566 d[n_] := IntegerDigits[n, 2];
%t A206566 t[n_] := Reverse[Array[d, 120][[n]]]
%t A206566 s[n_] := Position[t[n], 1]
%t A206566 t[m_, n_] := Length[Intersection[s[m], s[n]]]
%t A206566 TableForm[Table[t[m, n], {m, 1, 14},
%t A206566   {n, 1, 14}]] (* A206479 as a matrix *)
%t A206566 Flatten[Table[t[i, n + 1 - i], {n, 1, 14},
%t A206566   {i, 1, n}]]  (* A206479 as a sequence *)
%t A206566 u = Table[t[n - 1, m], {n, 3, 16}, {m, 1, n - 2}];
%t A206566 TableForm[u]   (* A206566 as a triangle *)
%t A206566 Flatten[u]     (* A206566 as a sequence *)
%t A206566 v[n_] := Table[t[k, n + 1], {k, 1, n}]
%t A206566 Table[Count[v[n], 0], {n, 1, 100}] (* A115478 *)
%Y A206566 Cf. A206479, A115478.
%K A206566 nonn,tabl,base
%O A206566 1,18
%A A206566 _Clark Kimberling_, Feb 09 2012