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A122750
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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.
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2
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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
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OFFSET
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0,5
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COMMENTS
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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
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LINKS
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EXAMPLE
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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
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MAPLE
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if type(n, 'even') then
if type(k, 'even') then
(-1)^k ;
else
2*(-1)^k ;
end if;
else
(-1)^(k+1) ;
end if;
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MATHEMATICA
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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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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