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A014987
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a(n) = (1 - (-6)^n)/7.
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16
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1, -5, 31, -185, 1111, -6665, 39991, -239945, 1439671, -8638025, 51828151, -310968905, 1865813431, -11194880585, 67169283511, -403015701065, 2418094206391, -14508565238345, 87051391430071, -522308348580425, 3133850091482551
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OFFSET
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1,2
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COMMENTS
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q-integers for q=-6.
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-1)=(-1)^n*charpoly(A,2). - 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).
G.f.: x/((1+6*x)*(1-x)).
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MAPLE
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a:=n->sum ((-6)^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, -6) for n in range(1, 22)] # Zerinvary Lajos, May 28 2009
(Magma) I:=[1, -5]; [n le 2 select I[n] else -5*Self(n-1)+6*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Oct 22 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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