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A084103
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Expansion of (1+x)^3/(1+x^3).
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3
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1, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3, 0, 3, 3, 0, -3, -3
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Partial sums are A084104.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,-1).
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FORMULA
| a(n)=sum{k=0..n, binomial(2n-k-1, k)(-1)^k*3(n-k)} - Paul Barry (pbarry(AT)wit.ie), Jan 21 2005
a(0)=1 and a(n)= 2*sqrt(3)*sin(n*Pi/3) [From Nour-Eddine Fahssi (fahssin(AT)yahoo.fr), Mar 04 2010]
Euler transform of length 6 sequence [ 3, -3, -1, 0, 0, 1]. - Michael Somos Feb 13 2011
a(n) = - a(-n) = 3 * A128834(n) except a(0) = 1. - Michael Somos Feb 13 2011
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EXAMPLE
| 1 + 3*x + 3*x^2 - 3*x^4 - 3*x^5 + 3*x^7 + 3*x^8 - 3*x^10 - 3*x^11 + ...
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PROG
| (PARI) {a(n) = (n==0) + [0, 3, 3, 0, -3, -3][n%6 + 1]} /* Michael Somos Feb 13 2011 */
(PARI) {a(n) = (n==0) - 3 * (-1)^n * kronecker(-3, n)} /* Michael Somos Feb 13 2011 */
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CROSSREFS
| Sequence in context: A098316 A160165 A084055 * A036477 A128164 A140686
Adjacent sequences: A084100 A084101 A084102 * A084104 A084105 A084106
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KEYWORD
| easy,sign
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), May 15 2003
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