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Search: id:A097164
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| A097164 |
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Expansion of (1+3x)/((1-x)(1-4x^2)). |
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+0
7
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| 1, 4, 8, 20, 36, 84, 148, 340, 596, 1364, 2388, 5460, 9556, 21844, 38228, 87380, 152916, 349524, 611668, 1398100, 2446676, 5592404, 9786708, 22369620, 39146836, 89478484, 156587348, 357913940, 626349396, 1431655764, 2505397588
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Partial sums of A084221. a(n)=A097163(n+1)/4. Third binomial transform is A097165.
a(n+1)=4*A097163(n) - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
See A133628 for an essentially identical sequence. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 08 2008
a(n)=a(n-1)+4a(n-2)-4a(n-3) ; a(0)=1,a(1)=4,a(2)=8. [From Paul Curtz (bpcrtz(AT)free.fr), Sep 07 2008]
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FORMULA
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a(n)=5*2^n/2-(-2)^n/6-4/3; a(n)=a(n-1)+4a(n-2)-4a(n-3).
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MAPLE
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a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=4*a[n-2]+4 od: seq(a[n], n=1..31); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 17 2008
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CROSSREFS
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Sequence in context: A034733 A152233 A053303 this_sequence A133628 A097940 A032280
Adjacent sequences: A097161 A097162 A097163 this_sequence A097165 A097166 A097167
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Jul 30 2004
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