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A014983
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a(n) = a(n-1) + (-3)^(n-1) = (1 - (-3)^n)/4. G.f.: x/((1-x)*(1+3*x)).
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20
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0, 1, -2, 7, -20, 61, -182, 547, -1640, 4921, -14762, 44287, -132860, 398581, -1195742, 3587227, -10761680, 32285041, -96855122, 290565367, -871696100, 2615088301, -7845264902, 23535794707, -70607384120, 211822152361, -635466457082
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| q-integers for q=-3.
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>=1, a(n)=(-1)^n*charpoly(A,0). [From Milan R. Janjic (agnus(AT)blic.net), Jan 27 2010]
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LINKS
| Index entries for sequences related to linear recurrences with constant coefficients
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 927
R. A. Sulanke, Moments of generalized Motzkin paths, J. Integer Sequences, Vol. 3 (2000), #00.1.
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FORMULA
| a(n) = the (1, 2)-th element of M^n, where M = ((1, 1, 1, -2), (1, 1, -2, 1), (1, -2, 1, 1), (-2, 1, 1, 1)). - Simone Severini (simoseve(AT)gmail.com), Nov 25 2004
a(0)=0, a(1)=1, a(n)=-2*a(n-1)+3*a(n-2) for n>1. [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 19 2009]
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MAPLE
| a:=n->sum ((-3)^j, j=0..n): seq(a(n), n=-1..25); # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2008]
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PROG
| (PARI) a(n)=(1-(-3)^n)/4
(Other) sage: [gaussian_binomial(n, 1, -3) for n in xrange(0, 27)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 28 2009]
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CROSSREFS
| A014983(n)=-(-1)^n*A015518(n).
A077925, A014985, A014986, A014987, A014989, A014990, A014991, A014992, A014993, A014994 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Dec 16 2008]
Sequence in context: A111017 A116408 * A015518 A083379 A000935 A035071
Adjacent sequences: A014980 A014981 A014982 * A014984 A014985 A014986
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KEYWORD
| sign,easy
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AUTHOR
| Olivier Gerard (olivier.gerard(AT)gmail.com)
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