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A106510
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Expansion of (1+x)^2/(1+x+x^2).
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15
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1, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1, 0, 1, -1
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OFFSET
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0,1
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COMMENTS
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Row sums of the Riordan array ((1+x)/(1+x+x^2),x/(1+x)), A106509.
Equals INVERT transform of (1, -2, 3, -4, 5, ...). - Gary W. Adamson, Oct 10 2008
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LINKS
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FORMULA
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a(n) = Sum_{k=0..n} Sum_{j=0..n-k} (-1)^j*binomial(2n-k-j, j)
Euler transform of length 3 sequence [ 1, -2, 1].
a(n) is multiplicative with a(3^e) = 0^e, a(p^e) = 1 if p == 1 (mod 3), a(p^e) = (-1)^e if p == 2 (mod 3).
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v) = 4 - 3*v - u * (4 - 2*v - u). (End)
a(-n) = a(n). a(n+3) = a(n) unless n = 0 or n = -3.
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EXAMPLE
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1 + x - x^2 + x^4 - x^5 + x^7 - x^8 + x^10 - x^11 + x^13 - x^14 + ...
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MATHEMATICA
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PROG
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(PARI) {a(n) = if( n==0, 1, [0, 1, -1][n%3 + 1])} \\ Michael Somos, Oct 15 2008
(PARI) {a(n) = if( n==0, 1, kronecker(-3, n))} \\ Michael Somos, Oct 15 2008
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CROSSREFS
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KEYWORD
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easy,sign,mult
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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