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Search: id:A106510
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| A106510 |
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Expansion of (1+x)^2/(1+x+x^2). |
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+0
8
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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; listen)
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OFFSET
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0,1
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COMMENT
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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,...). [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Oct 10 2008]
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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)}}
a(n) = A049347(n-1) if n>=1 . - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 08 2008
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.
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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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PROGRAM
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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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Sequence in context: A050072 A156707 A131309 this_sequence A163806 A163810 A163804
Adjacent sequences: A106507 A106508 A106509 this_sequence A106511 A106512 A106513
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KEYWORD
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easy,sign
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 04 2005
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