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,...

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, 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, 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

Offset: 1

Author

Clark Kimberling, Feb 09 2012

Keywords

• nonn
• tabl
• base

Comments

Row n consists of the first n terms of column n+1 of A206479, and (n-th row sum)=A115478(n+1).

Examples

			First ten rows:
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 1 1
0 1 1 0 0 1 1 1 1
1 1 2 0 1 1 2 1 2 2
		

Crossrefs

Cf. A206479, A115478.

Programs

Mathematica

d[n_] := IntegerDigits[n, 2];
t[n_] := Reverse[Array[d, 120][[n]]]
s[n_] := Position[t[n], 1]
t[m_, n_] := Length[Intersection[s[m], s[n]]]
TableForm[Table[t[m, n], {m, 1, 14},
  {n, 1, 14}]] (* A206479 as a matrix *)
Flatten[Table[t[i, n + 1 - i], {n, 1, 14},
  {i, 1, n}]]  (* A206479 as a sequence *)
u = Table[t[n - 1, m], {n, 3, 16}, {m, 1, n - 2}];
TableForm[u]   (* A206566 as a triangle *)
Flatten[u]     (* A206566 as a sequence *)
v[n_] := Table[t[k, n + 1], {k, 1, n}]
Table[Count[v[n], 0], {n, 1, 100}] (* A115478 *)