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

1,1

Links

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

Example

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; ...

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 *)

Prog

(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;
}
(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();
 ); }

Crossrefs

Related to A063865.

Sequence in context: A145362 A261092 A285960 * A265186 A248392 A188318

Adjacent sequences: A174597 A174598 A174599 * A174601 A174602 A174603

Keyword

nonn,tabl

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.

Status

approved