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A127236 A Thue-Morse binomial triangle. 6

%I #14 Jun 04 2020 08:16:50

%S 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 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 A Thue-Morse binomial triangle.

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

%H Robert Israel, <a href="/A127236/b127236.txt">Table of n, a(n) for n = 0..10010</a> (rows 0 to 140, flattened)

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

%e Triangle begins

%e 1;

%e 1, 1;

%e 1, 1, 1;

%e 1, 0, 0, 1;

%e 1, 1, 0, 1, 1;

%e 1, 0, 0, 0, 0, 1;

%e 1, 0, 0, 0, 0, 0, 1;

%e 1, 1, 1, 1, 1, 1, 1, 1;

%e 1, 1, 1, 1, 1, 1, 1, 1, 1;

%e 1, 0, 0, 1, 0, 0, 1, 0, 0, 1;

%e 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1;

%p tm:= proc(n) option remember;

%p if n::even then procname(n/2^padic:-ordp(n,2))

%p else 1 - procname((n-1)/2)

%p fi

%p end proc:

%p tm(0):= 0:

%p seq(seq(tm(binomial(n,k)),k=0..n),n=0..15); # _Robert Israel_, May 07 2019

%t T[n_, k_] := ThueMorse[Binomial[n, k]];

%t Table[T[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Jun 04 2020 *)

%Y Cf. A010060, A127237, A127238, A127239.

%K easy,nonn,tabl

%O 0,1

%A _Paul Barry_, Jan 10 2007

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)