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A268714 Square array A(i,j) = A006068(i) + A006068(j), read by antidiagonals.

%I A268714 #35 Apr 30 2021 12:38:53
%S A268714 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 A268714 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 A268714 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 A268714 Square array A(i,j) = A006068(i) + A006068(j), read by antidiagonals.
%H A268714 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 A268714 A(i,j) = A006068(i) + A006068(j).
%F A268714 A(i,j) = A006068(A268715(i,j)). - Corrected Mar 23 2017
%e A268714 The top left [0 .. 15] x [0 .. 15] section of the array:
%e A268714    0,  1,  3,  2,  7,  6,  4,  5, 15, 14, 12, 13,  8,  9, 11, 10
%e A268714    1,  2,  4,  3,  8,  7,  5,  6, 16, 15, 13, 14,  9, 10, 12, 11
%e A268714    3,  4,  6,  5, 10,  9,  7,  8, 18, 17, 15, 16, 11, 12, 14, 13
%e A268714    2,  3,  5,  4,  9,  8,  6,  7, 17, 16, 14, 15, 10, 11, 13, 12
%e A268714    7,  8, 10,  9, 14, 13, 11, 12, 22, 21, 19, 20, 15, 16, 18, 17
%e A268714    6,  7,  9,  8, 13, 12, 10, 11, 21, 20, 18, 19, 14, 15, 17, 16
%e A268714    4,  5,  7,  6, 11, 10,  8,  9, 19, 18, 16, 17, 12, 13, 15, 14
%e A268714    5,  6,  8,  7, 12, 11,  9, 10, 20, 19, 17, 18, 13, 14, 16, 15
%e A268714   15, 16, 18, 17, 22, 21, 19, 20, 30, 29, 27, 28, 23, 24, 26, 25
%e A268714   14, 15, 17, 16, 21, 20, 18, 19, 29, 28, 26, 27, 22, 23, 25, 24
%e A268714   12, 13, 15, 14, 19, 18, 16, 17, 27, 26, 24, 25, 20, 21, 23, 22
%e A268714   13, 14, 16, 15, 20, 19, 17, 18, 28, 27, 25, 26, 21, 22, 24, 23
%e A268714    8,  9, 11, 10, 15, 14, 12, 13, 23, 22, 20, 21, 16, 17, 19, 18
%e A268714    9, 10, 12, 11, 16, 15, 13, 14, 24, 23, 21, 22, 17, 18, 20, 19
%e A268714   11, 12, 14, 13, 18, 17, 15, 16, 26, 25, 23, 24, 19, 20, 22, 21
%e A268714   10, 11, 13, 12, 17, 16, 14, 15, 25, 24, 22, 23, 18, 19, 21, 20
%t A268714 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 A268714 (Scheme)
%o A268714 (define (A268714 n) (A268714bi (A002262 n) (A025581 n)))
%o A268714 (define (A268714bi row col) (+ (A006068 row) (A006068 col)))
%o A268714 (PARI)
%o A268714 \\ Produces the triangle when the array is read by antidiagonals
%o A268714 a(n) = if(n<2, n, 2*a(floor(n/2)) + (n%2 + a(floor(n/2))%2)%2); /* A006068 */
%o A268714 T(i,j) = a(i) + a(j);
%o A268714 for(i=0, 13, for(j=0, i, print1(T(i - j, j),", "););print();); \\ _Indranil Ghosh_, Mar 23 2017
%o A268714 (Python)
%o A268714 # Produces the triangle when the array is read by antidiagonals
%o A268714 def A006068(n):
%o A268714     return n if n<2 else 2*A006068(n//2) + (n%2 + A006068(n//2)%2)%2
%o A268714 def T(i,j): return A006068(i) + A006068(j)
%o A268714 for i in range(14):
%o A268714     print([T(i - j, j) for j in range(i + 1)]) # _Indranil Ghosh_, Mar 23 2017
%Y A268714 Cf. A003188, A268715.
%Y A268714 Cf. A006068 (row 0, column 0).
%Y A268714 Cf. A066194 (row 1, column 1).
%Y A268714 Cf. A268716 (main diagonal).
%Y A268714 Cf. also A268724.
%K A268714 nonn,tabl
%O A268714 0,4
%A A268714 _Antti Karttunen_, Feb 12 2016