A140586 Triangle t(n,m) read by rows: t(n,m) = binomial(n,m) if m <= floor(n/3) or m >= floor(2n/3), otherwise t(n,m)=0.

1, 1, 1, 1, 2, 1, 1, 3, 3, 1, 1, 4, 6, 4, 1, 1, 5, 0, 10, 5, 1, 1, 6, 15, 0, 15, 6, 1, 1, 7, 21, 0, 35, 21, 7, 1, 1, 8, 28, 0, 0, 56, 28, 8, 1, 1, 9, 36, 84, 0, 0, 84, 36, 9, 1, 1, 10, 45, 120, 0, 0, 210, 120, 45, 10, 1

Offset

1,5

Comments

Approximately one third of the coefficients in the middle of each row of the Pascal triangle are set to zero.

Row sums are 1, 2, 4, 8, 16, 22, 44, 93, 130, 260, 562, ...

Links

Table of n, a(n) for n=1..66.

Example

1;
1, 1;
1, 2, 1;
1, 3, 3, 1;
1, 4, 6, 4, 1;
1, 5, 0, 10, 5, 1;
1, 6, 15, 0, 15, 6, 1;
1, 7, 21,0, 35, 21, 7, 1;
1, 8, 28, 0, 0, 56, 28, 8, 1;
1, 9, 36, 84, 0, 0, 84, 36, 9, 1;
1, 10, 45, 120, 0, 0, 210, 120, 45, 10, 1;

Maple

A140586 := proc(n, k)
        if k <= floor(n/3) or  k >= floor(2*n/3) then
                binomial(n, k) ;
        else
               0 ;
        end if;
end proc:
seq(seq(A140586(n, m), m=0..n), n=0..14) ; # R. J. Mathar, Nov 10 2011

Mathematica

Table[Which[m<=Floor[n/3], Binomial[n, m], m>=Floor[2 n/3], Binomial[ n, m], True, 0], {n, 0, 10}, {m, 0, n}]//Flatten (* Harvey P. Dale, May 26 2016 *)

Crossrefs

Cf. A007318.

Sequence in context: A107065 A008975 A140280 * A339379 A095143 A242312

Adjacent sequences: A140583 A140584 A140585 * A140587 A140588 A140589

Keyword

nonn,tabl

Author

Roger L. Bagula and Gary W. Adamson, Jul 05 2008

Status

approved