A102037 Triangle of BitAnd(BitNot(n), k).

0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 2, 3, 0, 0, 0, 2, 2, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 2, 2, 4, 4, 6, 6, 0, 0, 0, 1, 0, 1, 4, 5, 4, 5, 0, 1, 0, 0, 0, 0, 0, 4, 4, 4, 4, 0, 0, 0, 0, 0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3, 0

Offset

0,13

Comments

As a logical operation on two variables this is also called the 'converse nonimplication'. - Peter Luschny, Sep 25 2021

Links

Table of n, a(n) for n=0..90.

Eric Weisstein's World of Mathematics, Sierpinski Sieve

Wikipedia, Converse nonimplication.

Example

Table starts:
[0] 0;
[1] 0, 0;
[2] 0, 1, 0;
[3] 0, 0, 0, 0;
[4] 0, 1, 2, 3, 0;
[5] 0, 0, 2, 2, 0, 0;
[6] 0, 1, 0, 1, 0, 1, 0;
[7] 0, 0, 0, 0, 0, 0, 0, 0;
[8] 0, 1, 2, 3, 4, 5, 6, 7, 0;
[9] 0, 0, 2, 2, 4, 4, 6, 6, 0, 0.

Maple

with(Bits): cnimp := (n, k) -> And(Not(n), k):
seq(print(seq(cnimp(n, k), k=0..n)), n = 0..12); # Peter Luschny, Sep 25 2021

Prog

(Julia)
using IntegerSequences
A102037Row(n) = [Bits("CNIMP", n, k) for k in 0:n]
for n in 0:20 println(A102037Row(n)) end  # Peter Luschny, Sep 25 2021

Crossrefs

Cf. A350094 (row sums), A268040 (array).

Other triangles: A080099 (AND), A080098 (OR), A051933 (XOR), A265705 (IMPL).

Sequence in context: A025109 A348710 A048735 * A286530 A152857 A097946

Adjacent sequences: A102034 A102035 A102036 * A102038 A102039 A102040

Keyword

nonn,easy,tabl

Author

Eric W. Weisstein, Dec 25 2004

Status

approved