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A035344
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Expansion of 1/((1-x)*(1-4*x+2*x^2)).
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4
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1, 5, 19, 67, 231, 791, 2703, 9231, 31519, 107615, 367423, 1254463, 4283007, 14623103, 49926399, 170459391, 581984767, 1987020287, 6784111615, 23162405887, 79081400319, 270000789503, 921840357375
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OFFSET
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0,2
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REFERENCES
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S. Bilotta, E. Pergola, R. Pinzani, S. Rinaldi, Recurrence relations versus succession rules, arXiv preprint arXiv:1301.2967, 2013. - From N. J. A. Sloane, Feb 12 2013
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LINKS
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Table of n, a(n) for n=0..22.
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FORMULA
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a(n)=2*A007052(n)-1. The sequence 0, 0, 1, 5, 19, ... is the binomial transform of the Pell numbers A000129, preceded by an additional 0. a(n)=(1+1/sqrt(2))(2+sqrt(2))^n+(1-1/sqrt(2))(2-sqrt(2))^n-1. - Paul Barry, Jul 16 2003
a(-1)=0, a(0)=1, a(n)=4*a(n-1)-2*a(n-2)+1 - Miklos Kristof, Mar 09 2005
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MAPLE
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a[ -1]:=0:a[0]:=1:for n from 1 to 50 do a[n]:=4*a[n-1]-2*a[n-2]+1 od: seq(a[n], n=0..50); (Kristof)
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MATHEMATICA
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Join[{a=1, b=5}, Table[c=4*b-2*a+1; a=b; b=c, {n, 60}]] (*From Vladimir Joseph Stephan Orlovsky, Feb 06 2011*)
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PROG
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(PARI) Vec(1/((1-x)*(1-4*x+2*x^2))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012
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CROSSREFS
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Partial sums of A007070.
Sequence in context: A067325 A121525 A163872 * A114277 A104496 A001435
Adjacent sequences: A035341 A035342 A035343 * A035345 A035346 A035347
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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