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

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, 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, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 0, 2, 0, 2

Offset: 1

Author

Craig Knecht, Jul 12 2015

Keywords

• nonn
• tabl
• easy

Comments

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

Examples

			Triangle T(n,k) begins:       Row sums
2;                                2
1,  1;                            2
0,  2,  0;                        2
1,  1,  1,  1;                    4
2,  0,  2,  0,  2;                6
1,  1,  1,  1,  1,  1;            6
0,  2,  0,  2,  0,  2,  0;        6
1,  1,  1,  1,  1,  1,  1,  1;    8
		

Links

• Craig Knecht, binary triangle rotated 180 degrees and superimposed on itself
• Craig Knecht, Color coded contributions of the individual triangles

Crossrefs

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

Programs

Maple

A257857 := proc(n,k)
    if type(n,'even') then
        1 ;
    elif type((n+1)/2+k,'even') then
        2 ;
    else
        0;
    end if;
end proc:

Formula

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

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

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