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A003986 Table of x OR y, where (x,y) = (0,0), (0,1), (1,0), (0,2), (1,1), (2,0), ... 73
0, 1, 1, 2, 1, 2, 3, 3, 3, 3, 4, 3, 2, 3, 4, 5, 5, 3, 3, 5, 5, 6, 5, 6, 3, 6, 5, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 7, 6, 7, 4, 7, 6, 7, 8, 9, 9, 7, 7, 5, 5, 7, 7, 9, 9, 10, 9, 10, 7, 6, 5, 6, 7, 10, 9, 10, 11, 11, 11, 11, 7, 7, 7, 7, 11, 11, 11, 11, 12, 11, 10, 11, 12, 7, 6, 7, 12, 11, 10, 11, 12, 13, 13, 11 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

T(x,y) = T(y,x) = A080098(x,y). - R. J. Mathar, May 28 2011

EXAMPLE

The upper left corner of the array starts in row x=0 with columns y>=0 as:

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

   1,  1,  3,  3,  5,  5,  7,  7,  9,  9, 11, 11, 13, ...

   2,  3,  2,  3,  6,  7,  6,  7, 10, 11, 10, 11, 14, ...

   3,  3,  3,  3,  7,  7,  7,  7, 11, 11, 11, 11, 15, ...

   4,  5,  6,  7,  4,  5,  6,  7, 12, 13, 14, 15, 12, ...

   5,  5,  7,  7,  5,  5,  7,  7, 13, 13, 15, 15, 13, ...

   6,  7,  6,  7,  6,  7,  6,  7, 14, 15, 14, 15, 14, ...

   7,  7,  7,  7,  7,  7,  7,  7, 15, 15, 15, 15, 15, ...

   8,  9, 10, 11, 12, 13, 14, 15,  8,  9, 10, 11, 12, ...

   9,  9, 11, 11, 13, 13, 15, 15,  9,  9, 11, 11, 13, ...

  10, 11, 10, 11, 14, 15, 14, 15, 10, 11, 10, 11, 14, ...

MAPLE

read("transforms") ;

A003986 := proc(x, y) ORnos(x, y) ; end proc:

for d from 0 to 12 do for x from 0 to d do printf("%d, ", A003986(x, d-x)) ; end do: end do: # R. J. Mathar, May 28 2011

MATHEMATICA

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

PROG

(Haskell)

import Data.Bits ((.|.))

a003986 n k = (n - k) .|. k :: Int

a003986_row n = map (a003986 n) [0..n]

a003986_tabl = map a003986_row [0..]

-- Reinhard Zumkeller, Aug 05 2014

(PARI)

tabl(nn) = {for(n=0, nn, for(k=0, n, print1(bitor(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. A003987 (XOR) and A004198 (AND). Cf. also A075173, A075175.

Antidiagonal sums are in A006583.

Sequence in context: A123243 A037193 A291615 * A123603 A228506 A228285

Adjacent sequences:  A003983 A003984 A003985 * A003987 A003988 A003989

KEYWORD

tabl,nonn,look

AUTHOR

Marc LeBrun

STATUS

approved

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Last modified December 5 18:40 EST 2020. Contains 338965 sequences. (Running on oeis4.)