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A268719
Triangular table T(n>=0,k=0..n) = A003188(A006068(n) + A006068(k)), read by rows as A(0,0), A(1,0), A(1,1), A(2,0), A(2,1), A(2,2), ...
3
0, 1, 3, 2, 6, 5, 3, 2, 7, 6, 4, 12, 15, 13, 9, 5, 4, 13, 12, 11, 10, 6, 7, 4, 5, 14, 15, 12, 7, 5, 12, 4, 10, 14, 13, 15, 8, 24, 27, 25, 29, 31, 26, 30, 17, 9, 8, 25, 24, 31, 30, 27, 26, 19, 18, 10, 11, 8, 9, 26, 27, 24, 25, 22, 23, 20, 11, 9, 24, 8, 30, 26, 25, 27, 18, 22, 21, 23, 12, 13, 14, 15, 8, 9, 10, 11, 28, 29, 30, 31, 24
OFFSET
0,3
FORMULA
T(n,k) = A003188(A006068(n) + A006068(k)).
a(n) = A268715(A003056(n), A002262(n)). [As a linear sequence.]
EXAMPLE
The first fifteen rows of the triangle:
0
1 3
2 6 5
3 2 7 6
4 12 15 13 9
5 4 13 12 11 10
6 7 4 5 14 15 12
7 5 12 4 10 14 13 15
8 24 27 25 29 31 26 30 17
9 8 25 24 31 30 27 26 19 18
10 11 8 9 26 27 24 25 22 23 20
11 9 24 8 30 26 25 27 18 22 21 23
12 13 14 15 8 9 10 11 28 29 30 31 24
13 15 10 14 24 8 11 9 20 28 31 29 25 27
14 10 9 11 27 25 8 24 23 21 28 20 26 30 29
MATHEMATICA
a88[n_] := BitXor[n, Floor[n/2]];
a68[n_] := BitXor @@ Table[Floor[n/2^m], {m, 0, Floor[Log[2, n]]}];
a68[0] = 0;
T[n_, k_] := a88[a68[n] + a68[k]];
Table[T[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-François Alcover, Nov 19 2019 *)
PROG
(Scheme) (define (A268719 n) (A268715bi (A003056 n) (A002262 n)))
(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): a003188(a006068(n) + a006068(k))
for n in range(21): print [T(n, k) for k in range(n + 1)] # Indranil Ghosh, Jun 07 2017
CROSSREFS
Cf. A001477 (left edge), A001969 (right edge).
Cf. A268720 (row sums).
Sequence in context: A304533 A090571 A088452 * A297878 A234922 A049777
KEYWORD
nonn,tabl
AUTHOR
Antti Karttunen, Feb 13 2016
STATUS
approved