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

1,1

Comments

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

Links

Table of n, a(n) for n=1..83.

Craig Knecht, binary triangle rotated 180 degrees and superimposed on itself

Craig Knecht, Color coded contributions of the individual triangles

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.

Example

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

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:

Crossrefs

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

Sequence in context: A180997 A143439 A105469 * A339871 A276806 A308427

Adjacent sequences: A257854 A257855 A257856 * A257858 A257859 A257860

Keyword

nonn,tabl,easy

Author

Craig Knecht, Jul 12 2015

Status

approved