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Search: id:A137199
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| A137199 |
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a(n)=a(n-1)+3a(n-2)+a(n-3). |
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+0
1
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| 1, 1, 1, 5, 9, 25, 57, 141, 337, 817, 1969, 4757, 11481, 27721, 66921, 161565, 390049, 941665, 2273377, 5488421, 13250217, 31988857, 77227929, 186444717, 450117361, 1086679441, 2623476241, 6333631925, 15290740089, 36915112105, 89120964297
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OFFSET
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0,4
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FORMULA
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O.g.f.: (-1+3*x^2)/{(1+x)(x^2+2*x-1)} . a(n) = (-1)^(n+1)+2*A000129(n-1) if n>=1. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2008
a(n)=-(-1)^n+[1+sqrt(2)]^n+(1/2)*sqrt(2)*[1-sqrt(2)]^n+[1-sqrt(2)]^n-(1/2)*[1+sqrt(2)]^n *sqrt(2), with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jun 09 2008
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CROSSREFS
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Cf. A097076.
Adjacent sequences: A137196 A137197 A137198 this_sequence A137200 A137201 A137202
Sequence in context: A147383 A127976 A147286 this_sequence A147512 A050359 A062812
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KEYWORD
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nonn
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AUTHOR
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Paul Curtz (bpcrtz(AT)free.fr), Mar 04 2008
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2008
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