A268714 - OEIS

%I #35 Apr 30 2021 12:38:53

%S 0,1,1,3,2,3,2,4,4,2,7,3,6,3,7,6,8,5,5,8,6,4,7,10,4,10,7,4,5,5,9,9,9,

%T 9,5,5,15,6,7,8,14,8,7,6,15,14,16,8,6,13,13,6,8,16,14,12,15,18,7,11,

%U 12,11,7,18,15,12,13,13,17,17,12,10,10,12,17,17,13,13,8,14,15,16,22,11,8,11,22,16,15,14,8,9,9,16,14,21,21,9,9,21,21,14,16,9,9

%N Square array A(i,j) = A006068(i) + A006068(j), read by antidiagonals.

%H Antti Karttunen, <a href="/A268714/b268714.txt">Table of n, a(n) for n = 0..15050; the first 173 antidiagonals of the array</a>

%F A(i,j) = A006068(i) + A006068(j).

%F A(i,j) = A006068(A268715(i,j)). - Corrected Mar 23 2017

%e The top left [0 .. 15] x [0 .. 15] section of the array:

%e    0,  1,  3,  2,  7,  6,  4,  5, 15, 14, 12, 13,  8,  9, 11, 10

%e    1,  2,  4,  3,  8,  7,  5,  6, 16, 15, 13, 14,  9, 10, 12, 11

%e    3,  4,  6,  5, 10,  9,  7,  8, 18, 17, 15, 16, 11, 12, 14, 13

%e    2,  3,  5,  4,  9,  8,  6,  7, 17, 16, 14, 15, 10, 11, 13, 12

%e    7,  8, 10,  9, 14, 13, 11, 12, 22, 21, 19, 20, 15, 16, 18, 17

%e    6,  7,  9,  8, 13, 12, 10, 11, 21, 20, 18, 19, 14, 15, 17, 16

%e    4,  5,  7,  6, 11, 10,  8,  9, 19, 18, 16, 17, 12, 13, 15, 14

%e    5,  6,  8,  7, 12, 11,  9, 10, 20, 19, 17, 18, 13, 14, 16, 15

%e   15, 16, 18, 17, 22, 21, 19, 20, 30, 29, 27, 28, 23, 24, 26, 25

%e   14, 15, 17, 16, 21, 20, 18, 19, 29, 28, 26, 27, 22, 23, 25, 24

%e   12, 13, 15, 14, 19, 18, 16, 17, 27, 26, 24, 25, 20, 21, 23, 22

%e   13, 14, 16, 15, 20, 19, 17, 18, 28, 27, 25, 26, 21, 22, 24, 23

%e    8,  9, 11, 10, 15, 14, 12, 13, 23, 22, 20, 21, 16, 17, 19, 18

%e    9, 10, 12, 11, 16, 15, 13, 14, 24, 23, 21, 22, 17, 18, 20, 19

%e   11, 12, 14, 13, 18, 17, 15, 16, 26, 25, 23, 24, 19, 20, 22, 21

%e   10, 11, 13, 12, 17, 16, 14, 15, 25, 24, 22, 23, 18, 19, 21, 20

%t A006068[n_] := BitXor @@ Table[Floor[n/2^m], {m, 0, Log[2, n]}]; A006068[0] = 0; A[i_, j_] := A006068[i] + A006068[j]; Table[A[i-j, j], {i, 0, 13}, {j, 0, i}] // Flatten (* _Jean-François Alcover_, Feb 17 2016 *)

%o (Scheme)

%o (define (A268714 n) (A268714bi (A002262 n) (A025581 n)))

%o (define (A268714bi row col) (+ (A006068 row) (A006068 col)))

%o (PARI)

%o \\ Produces the triangle when the array is read by antidiagonals

%o a(n) = if(n<2, n, 2*a(floor(n/2)) + (n%2 + a(floor(n/2))%2)%2); /* A006068 */

%o T(i,j) = a(i) + a(j);

%o for(i=0, 13, for(j=0, i, print1(T(i - j, j),", "););print();); \\ _Indranil Ghosh_, Mar 23 2017

%o (Python)

%o # Produces the triangle when the array is read by antidiagonals

%o def A006068(n):

%o     return n if n<2 else 2*A006068(n//2) + (n%2 + A006068(n//2)%2)%2

%o def T(i,j): return A006068(i) + A006068(j)

%o for i in range(14):

%o     print([T(i - j, j) for j in range(i + 1)]) # _Indranil Ghosh_, Mar 23 2017

%Y Cf. A003188, A268715.

%Y Cf. A006068 (row 0, column 0).

%Y Cf. A066194 (row 1, column 1).

%Y Cf. A268716 (main diagonal).

%Y Cf. also A268724.

%K nonn,tabl

%O 0,4

%A _Antti Karttunen_, Feb 12 2016