login
A127236
A Thue-Morse binomial triangle.
6
1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
0,1
COMMENTS
Row sums are A127237. Diagonal sums are A127238. Central coefficients T(2n,n) are A127239.
LINKS
Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened)
FORMULA
Number triangle T(n,k) = A010060(binomial(n,k)).
EXAMPLE
Triangle begins
1;
1, 1;
1, 1, 1;
1, 0, 0, 1;
1, 1, 0, 1, 1;
1, 0, 0, 0, 0, 1;
1, 0, 0, 0, 0, 0, 1;
1, 1, 1, 1, 1, 1, 1, 1;
1, 1, 1, 1, 1, 1, 1, 1, 1;
1, 0, 0, 1, 0, 0, 1, 0, 0, 1;
1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
MAPLE
tm:= proc(n) option remember;
if n::even then procname(n/2^padic:-ordp(n, 2))
else 1 - procname((n-1)/2)
fi
end proc:
tm(0):= 0:
seq(seq(tm(binomial(n, k)), k=0..n), n=0..15); # Robert Israel, May 07 2019
MATHEMATICA
T[n_, k_] := ThueMorse[Binomial[n, k]];
Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* Jean-François Alcover, Jun 04 2020 *)
CROSSREFS
KEYWORD
easy,nonn,tabl
AUTHOR
Paul Barry, Jan 10 2007
STATUS
approved