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A106510
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Expansion of (1+x)^2/(1+x+x^2).
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7
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| 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,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 10 2008]
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FORMULA
| a(n)=sum{k=0..n, sum{j=0..n-k, (-1)^j*binomial(2n-k-j, j)}}
a(n) = A049347(n-1) = A102283(n) if n>=1 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 07 2011
Euler transform of length 3 sequence [ 1, -2, 1]. - Michael Somos Oct 15 2008
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). - Michael Somos Oct 15 2008
G.f. A(x) satisfies 0=f(A(x), A(x^2)) where f(u, v) = 4 - 3*v - u * (4 - 2*v - u). - Michael Somos Oct 15 2008
a(-n) = a(n). a(n+3) = a(n) unless n=0 or n=-3.
a(n) = Sum_{k, 0<=k<=n} A128908(n,k)*(-1)^(n-k). - DELEHAM Philippe, Jan 22 2012
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EXAMPLE
| 1 + x - x^2 + x^4 - x^5 + x^7 - x^8 + x^10 - x^11 + x^13 - x^14 + ...
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PROG
| (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
| Sequence in context: A131309 * A163806 A163810 A163804 A181653 A155091
Adjacent sequences: A106507 A106508 A106509 * A106511 A106512 A106513
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 04 2005
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