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A145976
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Expansion of 1/(1-x*(1-7*x)).
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7
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1, 1, -6, -13, 29, 120, -83, -923, -342, 6119, 8513, -34320, -93911, 146329, 803706, -220597, -5846539, -4302360, 36623413, 66739933, -189623958, -656803489, 670564217, 5268188640, 574239121, -36303081359, -40322755206, 213798814307
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OFFSET
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0,3
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COMMENTS
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Row sums of Riordan array (1,x(1-7x)).
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LINKS
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Table of n, a(n) for n=0..27.
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FORMULA
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a(n)=a(n-1)-7*a(n-2); a(0)=1, a(1)=1. a(n)=Sum_{k, 0<=k<=n}A109466(n,k)*7^(n-k).
a(n)=-(1/18)*I*sqrt(3)*[(1/2)+(3/2)*I*sqrt(3)]^n+(1/18)*I*sqrt(3)*[(1/2)-(3/2)*I *sqrt(3)]^n+(1/2)*[(1/2)-(3/2)*I*sqrt(3)]^n+(1/2)*[(1/2)+(3/2)*I*sqrt(3)]^n, with n>=0 and I=sqrt(-1) [From Paolo P. Lava, Nov 18 2008]
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MATHEMATICA
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Join[{a=1, b=1}, Table[c=b-7*a; a=b; b=c, {n, 80}]] (*From Vladimir Joseph Stephan Orlovsky, Jan 22 2011*)
CoefficientList[Series[1/(1-x(1-7x)), {x, 0, 50}], x] (* or *) LinearRecurrence[{1, -7}, {1, 1}, 50] (* From Harvey P. Dale, May 11 2011 *)
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PROG
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(Sage) [lucas_number1(n, 1, 7) for n in xrange(1, 29)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
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CROSSREFS
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Cf. A010892, A107920, A106852, A106853, A106854, A145934
Sequence in context: A016071 A086652 A159694 * A101622 A192304 A147330
Adjacent sequences: A145973 A145974 A145975 * A145977 A145978 A145979
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KEYWORD
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sign
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AUTHOR
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Philippe DELEHAM, Oct 26 2008
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EXTENSIONS
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Corrected by Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009
Corrected by D. S. McNeil, Aug 20 2010
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STATUS
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approved
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