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A097164
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Expansion of (1+3x)/((1-x)(1-4x^2)).
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5
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,4,-4).
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FORMULA
| a(n)=5*2^n/2-(-2)^n/6-4/3; a(n)=a(n-1)+4a(n-2)-4a(n-3).
G.f. ( 1+3*x ) / ( (x-1)*(2*x+1)*(2*x-1) ). - R. J. Mathar, Jul 06 2011
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MAPLE
| 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
| Sequence in context: A152233 A053303 * A133628 A097940 A032280 A156303
Adjacent sequences: A097161 A097162 A097163 * A097165 A097166 A097167
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KEYWORD
| easy,nonn
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AUTHOR
| Paul Barry (pbarry(AT)wit.ie), Jul 30 2004
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