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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),... 81
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, 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, 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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,13

COMMENTS

Or, table of AND(i,j), i >= 0, j >= 0, read by antidiagonals. - N. J. A. Sloane, Feb 08 2016

Or, table of (i+j-Nimsum(i,j))/2) read by antidiagonals [Winning Ways, p. 75]. - N. J. A. Sloane, Feb 22 2019

REFERENCES

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982, see p. 75.

LINKS

T. D. Noe, Rows n=0..100 of triangle, flattened

EXAMPLE

The AND(i,j) table (shown without commas or spaces) begins:

0000000000000000000000000...

0101010101010101010101010...

0022002200220022002200220...

0123012301230123012301230...

0000444400004444000044440...

0101454501014545010145450...

0022446600224466002244660...

0123456701234567012345670...

0000000088888888000000008...

0101010189898989010101018...

The first few antidiagonals are:

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, 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,

...

- N. J. A. Sloane, Feb 08 2016

MAPLE

# Maple code for first M rows and columns of AND(i, j) table

M:=24;

f1:=n->[seq(ANDnos(i, n), i=0..M-1)];

for n from 0 to M-1 do lprint(f1(n)); od:

# N. J. A. Sloane, Feb 08 2016

MATHEMATICA

Table[BitAnd[k, n - k], {n, 0, 20}, {k, 0, n}] // Flatten (* Indranil Ghosh, Apr 01 2017 *)

PROG

(PARI)

tabl(nn) = {for(n=0, nn, for(k=0, n, print1(bitand(k, n - k), ", "); ); print(); ); };

tabl(20) \\ Indranil Ghosh, Apr 01 2017

(Python)

for n in range(21):

    print([k&(n - k) for k in range(n + 1)])

# Indranil Ghosh, Apr 01 2017

(C)

#include <stdio.h>

int main()

{

int n, k;

for (n=0; n<=20; n++){

    for(k=0; k<=n; k++){

        printf("%d, ", (k&(n - k)));

    }

    printf("\n");

}

return 0;

} /* Indranil Ghosh, Apr 01 2017 */

CROSSREFS

Cf. A003986 (OR) and A003987 (XOR). Cf. also A075173, A075175, A221146.

Sequence in context: A092606 A275948 A073253 * A324351 A116402 A093323

Adjacent sequences:  A004195 A004196 A004197 * A004199 A004200 A004201

KEYWORD

tabl,nonn,look

AUTHOR

David W. Wilson

STATUS

approved

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Last modified November 28 14:27 EST 2020. Contains 338724 sequences. (Running on oeis4.)