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A004198 Table of x AND y, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...

%I A004198 #39 Dec 28 2024 00:07:29
%S A004198 0,0,0,0,1,0,0,0,0,0,0,1,2,1,0,0,0,2,2,0,0,0,1,0,3,0,1,0,0,0,0,0,0,0,
%T A004198 0,0,0,1,2,1,4,1,2,1,0,0,0,2,2,4,4,2,2,0,0,0,1,0,3,4,5,4,3,0,1,0,0,0,
%U A004198 0,0,4,4,4,4,0,0,0,0,0,1,2,1,0,5,6,5,0,1,2,1,0,0,0,2,2,0,0,6,6,0,0,2,2,0,0,0,1,0
%N A004198 Table of x AND y, where (x,y) = (0,0),(0,1),(1,0),(0,2),(1,1),(2,0),...
%C A004198 Or, table of AND(i,j), i >= 0, j >= 0, read by antidiagonals. - _N. J. A. Sloane_, Feb 08 2016
%C A004198 Or, table of (i+j-Nimsum(i,j))/2 read by antidiagonals [Winning Ways, p. 75]. - _N. J. A. Sloane_, Feb 22 2019
%D A004198 E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 75.
%H A004198 T. D. Noe, <a href="/A004198/b004198.txt">Rows n=0..100 of triangle, flattened</a>
%e A004198 The AND(i,j) table (shown without commas or spaces) begins:
%e A004198 0000000000000000000000000...
%e A004198 0101010101010101010101010...
%e A004198 0022002200220022002200220...
%e A004198 0123012301230123012301230...
%e A004198 0000444400004444000044440...
%e A004198 0101454501014545010145450...
%e A004198 0022446600224466002244660...
%e A004198 0123456701234567012345670...
%e A004198 0000000088888888000000008...
%e A004198 0101010189898989010101018...
%e A004198 ...
%e A004198 The first few antidiagonals are:
%e A004198 0,
%e A004198 0, 0,
%e A004198 0, 1, 0,
%e A004198 0, 0, 0, 0,
%e A004198 0, 1, 2, 1, 0,
%e A004198 0, 0, 2, 2, 0, 0,
%e A004198 0, 1, 0, 3, 0, 1, 0,
%e A004198 0, 0, 0, 0, 0, 0, 0, 0,
%e A004198 0, 1, 2, 1, 4, 1, 2, 1, 0,
%e A004198 0, 0, 2, 2, 4, 4, 2, 2, 0, 0,
%e A004198 0, 1, 0, 3, 4, 5, 4, 3, 0, 1, 0,
%e A004198 ...
%e A004198 - _N. J. A. Sloane_, Feb 08 2016
%p A004198 # Maple code for first M rows and columns of AND(i,j) table
%p A004198 M:=24;
%p A004198 f1:=n->[seq(ANDnos(i,n),i=0..M-1)];
%p A004198 for n from 0 to M-1 do lprint(f1(n)); od:
%p A004198 # _N. J. A. Sloane_, Feb 08 2016
%t A004198 Table[BitAnd[k, n - k], {n, 0, 20}, {k, 0, n}] // Flatten (* _Indranil Ghosh_, Apr 01 2017 *)
%o A004198 (PARI)
%o A004198 tabl(nn) = {for(n=0, nn, for(k=0, n, print1(bitand(k, n - k), ", "); ); print(); ); };
%o A004198 tabl(20) \\ _Indranil Ghosh_, Apr 01 2017
%o A004198 (Python)
%o A004198 for n in range(21):
%o A004198     print([k&(n - k) for k in range(n + 1)])
%o A004198 # _Indranil Ghosh_, Apr 01 2017
%o A004198 (C)
%o A004198 #include <stdio.h>
%o A004198 int main()
%o A004198 {
%o A004198 int n, k;
%o A004198 for (n=0; n<=20; n++){
%o A004198     for(k=0; k<=n; k++){
%o A004198         printf("%d, ", (k&(n - k)));
%o A004198     }
%o A004198     printf("\n");
%o A004198 }
%o A004198 return 0;
%o A004198 } /* _Indranil Ghosh_, Apr 01 2017 */
%Y A004198 Cf. A003986 (OR) and A003987 (XOR). Cf. also A075173, A075175, A221146.
%K A004198 tabl,nonn,look
%O A004198 0,13
%A A004198 _David W. Wilson_