A122750 Triangle T(n,k) = (-1)^(k+1) if n is odd, = (-1)^k if n and k are even, = 2*(-1)^k if n is even and k is odd, 0<=k<=n.

1, -1, 1, 1, -2, 1, -1, 1, -1, 1, 1, -2, 1, -2, 1, -1, 1, -1, 1, -1, 1, 1, -2, 1, -2, 1, -2, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -2, 1, -2, 1, -2, 1, -2, 1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -2, 1, -2, 1, -2, 1, -2, 1, -2, 1

Offset: 0

Author

Roger L. Bagula, Sep 21 2006, Sep 04 2008

Keywords

• sign
• tabl
• easy

Comments

The row sums of the absolute values are 1+n*(5+(-1)^n)/4 = 1+A080512(n). - R. J. Mathar, May 12 2013

Examples

			Triangle begins:
   1
  -1,  1
   1, -2,  1
  -1,  1, -1,  1
   1, -2,  1, -2,  1
  -1,  1, -1,  1, -1,  1
   1, -2,  1, -2,  1, -2,  1
		

Programs

Maple

A122750 := proc(n,k)
    if type(n,'even') then
        if type(k,'even') then
            (-1)^k ;
        else
            2*(-1)^k ;
        end if;
    else
        (-1)^(k+1) ;
    end if;
end proc: # R. J. Mathar, May 12 2013

Mathematica

T[n_, k_] := If [Mod[n, 2] == 1, (-1)^(k + 1), (-1)^k*(1 + Mod[k, 2])]; a = Table[T[n, k], {n, 0, 10}, {k, 0, n}]; Flatten[a]
(* For the unsigned version: *) t[n_, m_] = 1 + Mod[n - m, 2]*Mod[m, 2]; a = Table[t[n, m], {n, 0, 10}, {m, 0, n}]; Flatten[a] (* Roger L. Bagula, Sep 06 2008 *)