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

0,6

Comments

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

Links

Rick L. Shepherd, Rows n=0..500 of triangle, flattened

Eric Weisstein's World of Mathematics, AND.

Example

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
...

Mathematica

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

Prog

(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
(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

Crossrefs

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

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

Sequence in context: A321198 A128584 A327853 * A268040 A127711 A336937

Adjacent sequences: A080096 A080097 A080098 * A080100 A080101 A080102

Keyword

nonn,easy,tabl,hear,look

Author

Reinhard Zumkeller, Jan 28 2003

Status

approved