A206479 Number of terms common to the binary expansions of m and n; a matrix by antidiagonals.

1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 2, 1, 2, 1, 2, 0, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 2, 2, 2, 0, 1, 1, 1, 0, 1, 1, 0, 0, 2, 2, 0, 0, 1, 1, 0, 1, 0, 2, 0, 1, 0, 3, 0, 1, 0, 2, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0

Offset

1,13

Links

Table of n, a(n) for n=1..99.

Example

Northwest corner (the antidiagonals can be read either
southwest or northeast, since the matrix is symmetric):
1 0 1 0 1 0 1 0 1 0
0 1 1 0 0 1 1 0 0 1
1 1 2 0 1 1 2 0 1 1
0 0 0 1 1 1 1 0 0 0
1 0 1 1 2 1 2 0 1 0
0 1 1 1 1 2 2 0 0 1
1 1 2 1 2 2 3 0 1 1
...
11 = 1 + 1*2 + 1*8 and 29 = 1 + 1*4 + 1*8 + 1*16,
so that T(11,29)=2.

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 *)

Crossrefs

Cf. A206566, A115478.

Sequence in context: A118917 A325045 A204293 * A219484 A060396 A353353

Adjacent sequences: A206476 A206477 A206478 * A206480 A206481 A206482

Keyword

nonn,tabl,base

Author

Clark Kimberling, Feb 09 2012

Status

approved