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A257857 Sequentially filled binary triangle rotated 180 degrees and then superimposed and added to the original triangle.

%I A257857 #38 Aug 05 2015 08:42:09
%S A257857 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 A257857 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 A257857 1,1,1,1,1,1,1,1,1,1,2,0,2,0,2
%N A257857 Sequentially filled binary triangle rotated 180 degrees and then superimposed and added to the original triangle.
%C A257857 The integers in the LINKS illustration hang like ornaments on a tree.
%H A257857 Craig Knecht, <a href="/A257857/a257857.jpg">binary triangle rotated 180 degrees and superimposed on itself</a>
%H A257857 Craig Knecht, <a href="/A257857/a257857_1.jpg">Color coded contributions of the individual triangles</a>
%F A257857 T(n,k)=1 if n even, 1<=k<=n.
%F A257857 T(n,k)=2 if n odd and (n+1)/2+k even, 1<=k<=n.
%F A257857 T(n,k)=0 if n odd and (n+1)/2+k odd, 1<=k<=n.
%e A257857 Triangle T(n,k) begins:       Row sums
%e A257857 2;                                2
%e A257857 1,  1;                            2
%e A257857 0,  2,  0;                        2
%e A257857 1,  1,  1,  1;                    4
%e A257857 2,  0,  2,  0,  2;                6
%e A257857 1,  1,  1,  1,  1,  1;            6
%e A257857 0,  2,  0,  2,  0,  2,  0;        6
%e A257857 1,  1,  1,  1,  1,  1,  1,  1;    8
%p A257857 A257857 := proc(n,k)
%p A257857     if type(n,'even') then
%p A257857         1 ;
%p A257857     elif type((n+1)/2+k,'even') then
%p A257857         2 ;
%p A257857     else
%p A257857         0;
%p A257857     end if;
%p A257857 end proc:
%Y A257857 For row sums for the three other variations of this build process, see A186421, A201629, A240828.
%K A257857 nonn,tabl,easy
%O A257857 1,1
%A A257857 _Craig Knecht_, Jul 12 2015