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

0,5

Comments

Original definition: A pattern triangular array with three coefficient states:{-2,-1,1} Rules: States {1,-1} going to States{1,-2,1} States{1,-2} going to {1,-1,1} States{-2,1} going to {-1,1,-1}.

The unsigned version is given by T(n,k)= 1 + mod(n-k,2) *mod(k,2). - Roger L. Bagula, Sep 06 2008

The row sums of the absolulte values are 1, 2, 4, 4, 7, 6, 10, 8, 13, 10, 16, ... - Roger L. Bagula, Sep 06 2008

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

Links

Table of n, a(n) for n=0..65.

Example

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

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

Crossrefs

Sequence in context: A276947 A178085 A078572 * A329041 A238744 A030421

Adjacent sequences: A122747 A122748 A122749 * A122751 A122752 A122753

Keyword

sign,tabl,easy

Author

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

Status

approved