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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. 2
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 (list; table; graph; refs; listen; history; text; internal format)
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 * A238744 A030421 A085021

Adjacent sequences:  A122747 A122748 A122749 * A122751 A122752 A122753

KEYWORD

sign,tabl,easy

AUTHOR

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

STATUS

approved

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Last modified October 18 23:39 EDT 2019. Contains 328211 sequences. (Running on oeis4.)