A080099 Triangle T(n,k) = n AND k, 0<=k<=n, bitwise logical AND, read by rows.

0, 0, 1, 0, 0, 2, 0, 1, 2, 3, 0, 0, 0, 0, 4, 0, 1, 0, 1, 4, 5, 0, 0, 2, 2, 4, 4, 6, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 1, 0, 1, 0, 1, 0, 1, 8, 9, 0, 0, 2, 2, 0, 0, 2, 2, 8, 8, 10, 0, 1, 2, 3, 0, 1, 2, 3, 8, 9, 10, 11, 0, 0, 0, 0, 4, 4, 4, 4, 8, 8, 8, 8, 12, 0, 1, 0, 1, 4, 5, 4, 5, 8, 9, 8, 9

Offset: 0

Author

Reinhard Zumkeller, Jan 28 2003

Keywords

• nonn
• easy
• tabl
• hear
• look

Comments

A080100(n) = number of numbers k such that n AND k = 0 in n-th row of the triangular array.

Examples

			Triangle starts:
0
0 1
0 0 2
0 1 2 3
0 0 0 0 4
0 1 0 1 4 5
0 0 2 2 4 4 6
0 1 2 3 4 5 6 7
...
		

Links

• Rick L. Shepherd, Rows n=0..500 of triangle, flattened
• Eric Weisstein's World of Mathematics, AND.

Crossrefs

Cf. A080100, A222423 (row sums), A004198 (array).

Other triangles: A080098 (OR), A051933 (XOR), A265705 (IMPL), A102037 (CNIMPL).

Programs

Haskell

import Data.Bits ((.&.))
a080099 n k = n .&. k :: Int
a080099_row n = map (a080099 n) [0..n]
a080099_tabl = map a080099_row [0..]
-- Reinhard Zumkeller, Aug 03 2014, Jul 05 2012

Mathematica

Column[Table[BitAnd[n, k], {n, 0, 15}, {k, 0, n}], Center] (* Alonso del Arte, Jun 19 2012 *)

PARI

T(n,k)=bitand(n,k) \\ Charles R Greathouse IV, Jan 26 2013

Python

def T(n, k): return n & k
print([T(n, k) for n in range(14) for k in range(n+1)]) # Michael S. Branicky, Dec 16 2021