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A268715
Square array A(i,j) = A003188(A006068(i) + A006068(j)), read by antidiagonals as A(0,0), A(0,1), A(1,0), A(0,2), A(1,1), A(2,0), ...
11
0, 1, 1, 2, 3, 2, 3, 6, 6, 3, 4, 2, 5, 2, 4, 5, 12, 7, 7, 12, 5, 6, 4, 15, 6, 15, 4, 6, 7, 7, 13, 13, 13, 13, 7, 7, 8, 5, 4, 12, 9, 12, 4, 5, 8, 9, 24, 12, 5, 11, 11, 5, 12, 24, 9, 10, 8, 27, 4, 14, 10, 14, 4, 27, 8, 10, 11, 11, 25, 25, 10, 15, 15, 10, 25, 25, 11, 11, 12, 9, 8, 24, 29, 14, 12, 14, 29, 24, 8, 9, 12, 13, 13, 24, 9, 31, 31, 13, 13, 31, 31, 9, 24, 13, 13
OFFSET
0,4
COMMENTS
Each row n is row A006068(n) of array A268820 without its A006068(n) initial terms.
FORMULA
A(i,j) = A003188(A006068(i) + A006068(j)) = A003188(A268714(i,j)).
A(row,col) = A268820(A006068(row), (A006068(row)+col)).
EXAMPLE
The top left [0 .. 15] x [0 .. 15] section of the array:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15
1, 3, 6, 2, 12, 4, 7, 5, 24, 8, 11, 9, 13, 15, 10, 14
2, 6, 5, 7, 15, 13, 4, 12, 27, 25, 8, 24, 14, 10, 9, 11
3, 2, 7, 6, 13, 12, 5, 4, 25, 24, 9, 8, 15, 14, 11, 10
4, 12, 15, 13, 9, 11, 14, 10, 29, 31, 26, 30, 8, 24, 27, 25
5, 4, 13, 12, 11, 10, 15, 14, 31, 30, 27, 26, 9, 8, 25, 24
6, 7, 4, 5, 14, 15, 12, 13, 26, 27, 24, 25, 10, 11, 8, 9
7, 5, 12, 4, 10, 14, 13, 15, 30, 26, 25, 27, 11, 9, 24, 8
8, 24, 27, 25, 29, 31, 26, 30, 17, 19, 22, 18, 28, 20, 23, 21
9, 8, 25, 24, 31, 30, 27, 26, 19, 18, 23, 22, 29, 28, 21, 20
10, 11, 8, 9, 26, 27, 24, 25, 22, 23, 20, 21, 30, 31, 28, 29
11, 9, 24, 8, 30, 26, 25, 27, 18, 22, 21, 23, 31, 29, 20, 28
12, 13, 14, 15, 8, 9, 10, 11, 28, 29, 30, 31, 24, 25, 26, 27
13, 15, 10, 14, 24, 8, 11, 9, 20, 28, 31, 29, 25, 27, 30, 26
14, 10, 9, 11, 27, 25, 8, 24, 23, 21, 28, 20, 26, 30, 29, 31
15, 14, 11, 10, 25, 24, 9, 8, 21, 20, 29, 28, 27, 26, 31, 30
MATHEMATICA
A003188[n_] := BitXor[n, Floor[n/2]]; A006068[n_] := BitXor @@ Table[Floor[ n/2^m], {m, 0, Log[2, n]}]; A006068[0]=0; A[i_, j_] := A003188[A006068[i] + A006068[j]]; Table[A[i-j, j], {i, 0, 13}, {j, 0, i}] // Flatten (* Jean-François Alcover, Feb 17 2016 *)
PROG
(Scheme)
(define (A268715 n) (A268715bi (A002262 n) (A025581 n)))
(define (A268715bi row col) (A003188 (+ (A006068 row) (A006068 col))))
;; Alternatively, extracting data from array A268820:
(define (A268715bi row col) (A268820bi (A006068 row) (+ (A006068 row) col)))
(Python)
def a003188(n): return n^(n>>1)
def a006068(n):
s=1
while True:
ns=n>>s
if ns==0: break
n=n^ns
s<<=1
return n
def T(n, k): return a003188(a006068(n) + a006068(k))
for n in range(21): print([T(n - k, k) for k in range(n + 1)]) # Indranil Ghosh, Jun 07 2017
CROSSREFS
Main diagonal: A001969.
Row 0, column 0: A001477.
Row 1, column 1: A268717.
Antidiagonal sums: A268837.
Cf. A268719 (the lower triangular section).
Cf. also A268725.
Sequence in context: A085208 A332553 A257302 * A085211 A085212 A079025
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Feb 12 2016
STATUS
approved