A174600 T(n,k) = 1 if the sum of +-k..+-n with arbitrary signs never equals zero, = 0 otherwise (lower triangle).

1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1

Offset: 1

Author

R. H. Hardin Mar 23 2010, with formula and reference from Franklin T. Adams-Watters and Olivier Gérard, on the Sequence Fans Mailing list

Keywords

• nonn
• tabl

Examples

			Triangle begins
1;
1, 1;
0, 1, 1;
0, 1, 1, 1;
1, 0, 1, 1, 1;
1, 0, 0, 1, 1, 1;
0, 1, 1, 0, 1, 1, 1;
0, 1, 1, 0, 0, 1, 1, 1;
1, 0, 0, 1, 1, 0, 1, 1, 1;
1, 0, 0, 1, 1, 1, 0, 1, 1, 1; ...
		

Links

• R. H. Hardin, Table of n, a(n) for n=1..4950

Crossrefs

Related to A063865.

Programs

AWK

{ for(n=1; n<10; n++)
        for(k=1; k<=n; k++)
            print ++i, T(n,k);
}
function T(n,k) {
    if ( int((n+1)/2)%2 != int(k/2)%2 ) return 1;
    else if ( (n-k)%2 == 0 ) {
        if ( k > ((n-k)/2)^2 ) return 1;
        else return 0;
    }
    else return 0;
}

Mathematica

t[n_, k_] := If[Mod[Floor[(n+1)/2], 2] != Mod[Floor[k/2], 2], 1, If[Mod[n-k, 2] == 0, If[k > ((n-k)/2)^2, 1, 0], 0]]; Flatten[Table[t[n, k], {n, 1, 15}, {k, 1, n}]][[;; 108]] (* Jean-François Alcover, Jul 11 2011, after awk program *)

PARI

T(n,k)=
{
    if ( ((n+1)\2)%2 != (k\2)%2,
        return(1);
    , /* else */
        if ( (n-k)%2 == 0,
            if ( k > ((n-k)/2)^2, return(1), return(0) );
        , /* else */
            return(0);
        );
    );
}
{ for(n=1, 10, /* show triangle */
    for(k=1,n,
        print1(T(n,k),", ");
    );
    print();
 ); }