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A014985
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q-integers for q=-4.
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13
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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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]
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-3, A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=2, a(n-1)=(-1)^n*charpoly(A,1). [From Milan R. Janjic (agnus(AT)blic.net), Jan 27 2010]
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REFERENCES
| 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
| 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
| 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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PROG
| (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
| A077925, A014983, A014986, A014987, A014989, A014990, A014991, A014992, A014993, A014994 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2008]
Sequence in context: A163774 A197074 * A015521 A146279 A098619 A086608
Adjacent sequences: A014982 A014983 A014984 * A014986 A014987 A014988
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KEYWORD
| sign,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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