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Pascal's tetrahedron of trinomial coefficients (A046816) read mod 2.
2

%I #24 May 06 2016 06:54:36

%S 1,1,1,1,1,0,0,1,0,1,1,1,1,1,0,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0,0,0,

%T 1,1,1,1,0,0,0,0,0,0,0,1,0,0,0,1,1,1,0,0,1,1,1,0,0,1,0,1,0,0,0,0,1,0,

%U 0,0,1,0,0,0,0,0,0,1,0,1,0,1,0,1

%N Pascal's tetrahedron of trinomial coefficients (A046816) read mod 2.

%C Might be called Sierpinski's tetrahedron, by analogy with A047999.

%C The number of 1's in the n-th slice is A048883(n), 3^wt(n). - _N. J. A. Sloane_, Feb 14 2016

%H R. J. Mathar, <a href="/A268240/b268240.txt">Table of n, a(n) for n = 0..5455</a>

%p # Pascal tetrahedron mod 2 A268240 (based on program in A046816):

%p A268240 := proc(i,j,k)

%p modp(A046816(i,j,k),2) ;

%p end proc:

%p seq(seq(seq(A268240(i, j, k), j=0..i), i=0..k), k=0..8);

%p # Another version from _N. J. A. Sloane_, Feb 14 2016:

%p MC:=(i,j,k) -> (i+j+k)!/(i!*j!*k!);

%p PT:=proc(n) local T,i,j,k; T:=0;

%p for i from n by -1 to 0 do

%p for j from n-i by -1 to 0 do lprint((MC(i,j,n-i-j) mod 2)); od: od: end;

%p for n from 0 to 8 do lprint("n=",n); PT(n); od:

%Y Cf. A007318, A047999, A046816, A048883.

%K nonn,tabf

%O 0

%A _Benoit Cloitre_ and _N. J. A. Sloane_, Feb 05 2016