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

0,1

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

Cf. A010060, A127237, A127238, A127239.

Sequence in context: A204177 A185917 A143104 * A117947 A175860 A351956

Adjacent sequences: A127233 A127234 A127235 * A127237 A127238 A127239

Keyword

easy,nonn,tabl

Author

Paul Barry, Jan 10 2007

Status

approved