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Search: id:A014985
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| 1, -3, 13, -51, 205, -819, 3277, -13107, 52429, -209715, 838861, -3355443, 13421773, -53687091, 214748365, -858993459, 3435973837, -13743895347, 54975581389, -219902325555, 879609302221, -3518437208883, 14073748835533
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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In Penrose's book, presented as partial sums of the series for 1/(1-x^2) evaluated at x=2. [From Olivier GERARD (olivier.gerard(AT)gmail.com), May 22 2009]
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REFERENCES
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Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, pages 79-80. [From Olivier GERARD (olivier.gerard(AT)gmail.com), May 22 2009]
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FORMULA
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a(n) = a(n-1) + q^{(n-1)} = {(q^n - 1) / (q - 1)}
G.f.: 1/(1+3x-4x^2); a(n)=sum{k=0..floor(n/2), C(n-k,k)4^k*(-3)^(n-2k)}; - Paul Barry (pbarry(AT)wit.ie), Jan 12 2007
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MAPLE
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a:=n->sum ((-4)^j, j=0..n): seq(a(n), n=0..25); [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2008]
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PROGRAM
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(Other) sage: [gaussian_binomial(n, 1, -4) for n in xrange(1, 24)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
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CROSSREFS
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A077925, A014983, A014986, A014987, A014989, A014990, A014991, A014992, A014993, A014994 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2008]
Sequence in context: A101052 A016064 A163774 this_sequence A015521 A146279 A098619
Adjacent sequences: A014982 A014983 A014984 this_sequence A014986 A014987 A014988
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KEYWORD
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sign,easy
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AUTHOR
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Olivier Gerard (olivier.gerard(AT)gmail.com)
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