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

Author

Eric W. Weisstein, Dec 25 2004

Keywords

• nonn
• easy
• tabl

Comments

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

Examples

			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.
		

Links

• Eric Weisstein's World of Mathematics, Sierpinski Sieve
• Wikipedia, Converse nonimplication.

Crossrefs

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

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

Programs

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

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