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A014986
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a(n) = (1 - (-5)^n)/6.
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13
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1, -4, 21, -104, 521, -2604, 13021, -65104, 325521, -1627604, 8138021, -40690104, 203450521, -1017252604, 5086263021, -25431315104, 127156575521, -635782877604, 3178914388021, -15894571940104, 79472859700521
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OFFSET
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1,2
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COMMENTS
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q-integers for q = -5.
Let A be the Hessenberg matrix of order n, defined by: A[1,j]=1, A[i,i]:=-5, (i>1), A[i,i-1]=-1, and A[i,j]=0 otherwise. Then, for n>=1, a(n)=det(A). - Milan Janjic, Jan 27 2010
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LINKS
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FORMULA
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a(n) = a(n-1) + q^(n-1) = (q^n - 1) / (q - 1).
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MAPLE
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a:=n->sum ((-5)^j, j=0..n): seq(a(n), n=0..25); # Zerinvary Lajos, Dec 16 2008
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MATHEMATICA
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PROG
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(Sage) [gaussian_binomial(n, 1, -5) for n in range(1, 22)] # Zerinvary Lajos, May 28 2009
(Magma) I:=[1, -4]; [n le 2 select I[n] else -4*Self(n-1)+5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Jun 19 2012
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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