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Sequentially filled binary triangle rotated 180 degrees and then superimposed and added to the original triangle.
1

%I #38 Aug 05 2015 08:42:09

%S 2,1,1,0,2,0,1,1,1,1,2,0,2,0,2,1,1,1,1,1,1,0,2,0,2,0,2,0,1,1,1,1,1,1,

%T 1,1,2,0,2,0,2,0,2,0,2,1,1,1,1,1,1,1,1,1,1,0,2,0,2,0,2,0,2,0,2,0,1,1,

%U 1,1,1,1,1,1,1,1,1,1,2,0,2,0,2

%N Sequentially filled binary triangle rotated 180 degrees and then superimposed and added to the original triangle.

%C The integers in the LINKS illustration hang like ornaments on a tree.

%H Craig Knecht, <a href="/A257857/a257857.jpg">binary triangle rotated 180 degrees and superimposed on itself</a>

%H Craig Knecht, <a href="/A257857/a257857_1.jpg">Color coded contributions of the individual triangles</a>

%F T(n,k)=1 if n even, 1<=k<=n.

%F T(n,k)=2 if n odd and (n+1)/2+k even, 1<=k<=n.

%F T(n,k)=0 if n odd and (n+1)/2+k odd, 1<=k<=n.

%e Triangle T(n,k) begins: Row sums

%e 2; 2

%e 1, 1; 2

%e 0, 2, 0; 2

%e 1, 1, 1, 1; 4

%e 2, 0, 2, 0, 2; 6

%e 1, 1, 1, 1, 1, 1; 6

%e 0, 2, 0, 2, 0, 2, 0; 6

%e 1, 1, 1, 1, 1, 1, 1, 1; 8

%p A257857 := proc(n,k)

%p if type(n,'even') then

%p 1 ;

%p elif type((n+1)/2+k,'even') then

%p 2 ;

%p else

%p 0;

%p end if;

%p end proc:

%Y For row sums for the three other variations of this build process, see A186421, A201629, A240828.

%K nonn,tabl,easy

%O 1,1

%A _Craig Knecht_, Jul 12 2015