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

%I A080099 #32 Feb 16 2025 08:32:48
%S A080099 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,
%T A080099 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,
%U A080099 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
%N A080099 Triangle T(n,k) = n AND k, 0<=k<=n, bitwise logical AND, read by rows.
%C A080099 A080100(n) = number of numbers k such that n AND k = 0 in n-th row of the triangular array.
%H A080099 Rick L. Shepherd, <a href="/A080099/b080099.txt">Rows n=0..500 of triangle, flattened</a>
%H A080099 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AND.html">AND.</a>
%e A080099 Triangle starts:
%e A080099 0
%e A080099 0 1
%e A080099 0 0 2
%e A080099 0 1 2 3
%e A080099 0 0 0 0 4
%e A080099 0 1 0 1 4 5
%e A080099 0 0 2 2 4 4 6
%e A080099 0 1 2 3 4 5 6 7
%e A080099 ...
%t A080099 Column[Table[BitAnd[n, k], {n, 0, 15}, {k, 0, n}], Center] (* _Alonso del Arte_, Jun 19 2012 *)
%o A080099 (Haskell)
%o A080099 import Data.Bits ((.&.))
%o A080099 a080099 n k = n .&. k :: Int
%o A080099 a080099_row n = map (a080099 n) [0..n]
%o A080099 a080099_tabl = map a080099_row [0..]
%o A080099 -- _Reinhard Zumkeller_, Aug 03 2014, Jul 05 2012
%o A080099 (PARI) T(n,k)=bitand(n,k) \\ _Charles R Greathouse IV_, Jan 26 2013
%o A080099 (Python)
%o A080099 def T(n, k): return n & k
%o A080099 print([T(n, k) for n in range(14) for k in range(n+1)]) # _Michael S. Branicky_, Dec 16 2021
%Y A080099 Cf. A080100, A222423 (row sums), A004198 (array).
%Y A080099 Other triangles: A080098 (OR), A051933 (XOR), A265705 (IMPL), A102037 (CNIMPL).
%K A080099 nonn,easy,tabl,hear,look
%O A080099 0,6
%A A080099 _Reinhard Zumkeller_, Jan 28 2003