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A102037 Triangle of BitAnd(BitNot(n), k). 5

%I #19 Dec 17 2021 01:40:33

%S 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,

%T 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,

%U 0,0,4,4,4,4,0,0,0,0,0,1,2,3,0,1,2,3,0,1,2,3,0

%N Triangle of BitAnd(BitNot(n), k).

%C As a logical operation on two variables this is also called the 'converse nonimplication'. - _Peter Luschny_, Sep 25 2021

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiSieve.html">Sierpinski Sieve</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Converse_nonimplication">Converse nonimplication</a>.

%e Table starts:

%e [0] 0;

%e [1] 0, 0;

%e [2] 0, 1, 0;

%e [3] 0, 0, 0, 0;

%e [4] 0, 1, 2, 3, 0;

%e [5] 0, 0, 2, 2, 0, 0;

%e [6] 0, 1, 0, 1, 0, 1, 0;

%e [7] 0, 0, 0, 0, 0, 0, 0, 0;

%e [8] 0, 1, 2, 3, 4, 5, 6, 7, 0;

%e [9] 0, 0, 2, 2, 4, 4, 6, 6, 0, 0.

%p with(Bits): cnimp := (n, k) -> And(Not(n), k):

%p seq(print(seq(cnimp(n,k), k=0..n)), n = 0..12); # _Peter Luschny_, Sep 25 2021

%o (Julia)

%o using IntegerSequences

%o A102037Row(n) = [Bits("CNIMP", n, k) for k in 0:n]

%o for n in 0:20 println(A102037Row(n)) end # _Peter Luschny_, Sep 25 2021

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

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

%K nonn,easy,tabl

%O 0,13

%A _Eric W. Weisstein_, Dec 25 2004

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Last modified June 29 23:48 EDT 2024. Contains 373856 sequences. (Running on oeis4.)