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

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, 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, 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

Offset: 0

Author

Antti Karttunen, Feb 12 2016

Keywords

• nonn
• tabl

Examples

			The top left [0 .. 15] x [0 .. 15] section of the array:
   0,  1,  3,  2,  7,  6,  4,  5, 15, 14, 12, 13,  8,  9, 11, 10
   1,  2,  4,  3,  8,  7,  5,  6, 16, 15, 13, 14,  9, 10, 12, 11
   3,  4,  6,  5, 10,  9,  7,  8, 18, 17, 15, 16, 11, 12, 14, 13
   2,  3,  5,  4,  9,  8,  6,  7, 17, 16, 14, 15, 10, 11, 13, 12
   7,  8, 10,  9, 14, 13, 11, 12, 22, 21, 19, 20, 15, 16, 18, 17
   6,  7,  9,  8, 13, 12, 10, 11, 21, 20, 18, 19, 14, 15, 17, 16
   4,  5,  7,  6, 11, 10,  8,  9, 19, 18, 16, 17, 12, 13, 15, 14
   5,  6,  8,  7, 12, 11,  9, 10, 20, 19, 17, 18, 13, 14, 16, 15
  15, 16, 18, 17, 22, 21, 19, 20, 30, 29, 27, 28, 23, 24, 26, 25
  14, 15, 17, 16, 21, 20, 18, 19, 29, 28, 26, 27, 22, 23, 25, 24
  12, 13, 15, 14, 19, 18, 16, 17, 27, 26, 24, 25, 20, 21, 23, 22
  13, 14, 16, 15, 20, 19, 17, 18, 28, 27, 25, 26, 21, 22, 24, 23
   8,  9, 11, 10, 15, 14, 12, 13, 23, 22, 20, 21, 16, 17, 19, 18
   9, 10, 12, 11, 16, 15, 13, 14, 24, 23, 21, 22, 17, 18, 20, 19
  11, 12, 14, 13, 18, 17, 15, 16, 26, 25, 23, 24, 19, 20, 22, 21
  10, 11, 13, 12, 17, 16, 14, 15, 25, 24, 22, 23, 18, 19, 21, 20
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..15050; the first 173 antidiagonals of the array

Crossrefs

Cf. A003188, A268715.

Cf. A006068 (row 0, column 0).

Cf. A066194 (row 1, column 1).

Cf. A268716 (main diagonal).

Cf. also A268724.

Programs

Mathematica

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 *)

PARI

\\ Produces the triangle when the array is read by antidiagonals
a(n) = if(n<2, n, 2*a(floor(n/2)) + (n%2 + a(floor(n/2))%2)%2); /* A006068 */
T(i,j) = a(i) + a(j);
for(i=0, 13, for(j=0, i, print1(T(i - j, j),", "););print();); \\ Indranil Ghosh, Mar 23 2017

Python

# Produces the triangle when the array is read by antidiagonals
def A006068(n):
    return n if n<2 else 2*A006068(n//2) + (n%2 + A006068(n//2)%2)%2
def T(i,j): return A006068(i) + A006068(j)
for i in range(14):
    print([T(i - j, j) for j in range(i + 1)]) # Indranil Ghosh, Mar 23 2017

Scheme

(define (A268714 n) (A268714bi (A002262 n) (A025581 n)))
(define (A268714bi row col) (+ (A006068 row) (A006068 col)))

Formula

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

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