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A127236 A Thue-Morse binomial triangle.

%I A127236 #14 Jun 04 2020 08:16:50
%S A127236 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,
%T A127236 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
%N A127236 A Thue-Morse binomial triangle.
%C A127236 Row sums are A127237. Diagonal sums are A127238. Central coefficients T(2n,n) are A127239.
%H A127236 Robert Israel, <a href="/A127236/b127236.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened)
%F A127236 Number triangle T(n,k) = A010060(binomial(n,k)).
%e A127236 Triangle begins
%e A127236   1;
%e A127236   1, 1;
%e A127236   1, 1, 1;
%e A127236   1, 0, 0, 1;
%e A127236   1, 1, 0, 1, 1;
%e A127236   1, 0, 0, 0, 0, 1;
%e A127236   1, 0, 0, 0, 0, 0, 1;
%e A127236   1, 1, 1, 1, 1, 1, 1, 1;
%e A127236   1, 1, 1, 1, 1, 1, 1, 1, 1;
%e A127236   1, 0, 0, 1, 0, 0, 1, 0, 0, 1;
%e A127236   1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;
%p A127236 tm:= proc(n) option remember;
%p A127236   if n::even then procname(n/2^padic:-ordp(n,2))
%p A127236   else 1 - procname((n-1)/2)
%p A127236   fi
%p A127236 end proc:
%p A127236 tm(0):= 0:
%p A127236 seq(seq(tm(binomial(n,k)),k=0..n),n=0..15); # _Robert Israel_, May 07 2019
%t A127236 T[n_, k_] := ThueMorse[Binomial[n, k]];
%t A127236 Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 04 2020 *)
%Y A127236 Cf. A010060, A127237, A127238, A127239.
%K A127236 easy,nonn,tabl
%O A127236 0,1
%A A127236 _Paul Barry_, Jan 10 2007