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 A035344 Expansion of 1/((1-x)*(1-4*x+2*x^2)). 4
 1, 5, 19, 67, 231, 791, 2703, 9231, 31519, 107615, 367423, 1254463, 4283007, 14623103, 49926399, 170459391, 581984767, 1987020287, 6784111615, 23162405887, 79081400319, 270000789503, 921840357375 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES 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 LINKS FORMULA 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 MAPLE 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) MATHEMATICA 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*) PROG (PARI) Vec(1/((1-x)*(1-4*x+2*x^2))+O(x^99)) \\ Charles R Greathouse IV, Sep 24 2012 CROSSREFS Partial sums of A007070. Sequence in context: A067325 A121525 A163872 * A114277 A104496 A001435 Adjacent sequences:  A035341 A035342 A035343 * A035345 A035346 A035347 KEYWORD nonn,easy AUTHOR STATUS approved

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