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Search: id:A035344
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| A035344 |
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Expansion of 1/((1-x)*(1-4*x+2*x^2)). |
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+0
2
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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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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 (pbarry(AT)wit.ie), Jul 16 2003
a(-1)=0, a(0)=1, a(n)=4*a(n-1)-2*a(n-2)+1 - Miklos Kristof (kristmikl(AT)freemail.hu), 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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CROSSREFS
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Partial sums of A007070.
Sequence in context: A005021 A067325 A121525 this_sequence A114277 A104496 A001435
Adjacent sequences: A035341 A035342 A035343 this_sequence A035345 A035346 A035347
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KEYWORD
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nonn
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AUTHOR
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njas
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