A127236 A Thue-Morse binomial triangle.

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

Author

Paul Barry, Jan 10 2007

Keywords

• easy
• nonn
• tabl

Comments

Row sums are A127237. Diagonal sums are A127238. Central coefficients T(2n,n) are A127239.

Examples

			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;
		

Links

• Robert Israel, Table of n, a(n) for n = 0..10010 (rows 0 to 140, flattened)

Crossrefs

Cf. A010060, A127237, A127238, A127239.

Programs

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 *)

Formula

Number triangle T(n,k) = A010060(binomial(n,k)).