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Search: id:A137221
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| A137221 |
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a(n)=5a(n-1)-9a(n-2)+8a(n-3)-4a(n-4). |
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+0
2
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| 0, 0, 0, 1, 5, 16, 43, 107, 256, 597, 1365, 3072, 6827, 15019, 32768, 70997, 152917, 327680, 699051, 1485483, 3145728, 6640981, 13981013, 29360128, 61516459, 128625323, 268435456, 559240533, 1163220309, 2415919104, 5010795179
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OFFSET
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0,5
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FORMULA
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Binomial transform of A002264; a(n+1)-2a(n)=A024495.
O.g.f.: x^3/{(x^2-x+1)(-1+2*x)^2} . a(n)=[ -3*2^n+A001787(n+1)+2*A010892(n)]/6. - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Mar 17 2008
a(n)=(1/6)*{1/2-(1/2)*I*sqrt(3)}^n+(1/6)*{1/2+(1/2)*I*sqrt(3)}^n-(1/3)*2^n+[(1/18)*I]*{1/2-(1 /2)*I*sqrt(3)}^n*sqrt(3)+(1/6)*2^n*n-[(1/18)*I]*{1/2+(1/2)*I*sqrt(3)}^n*sqrt(3), with n>=0 and I=sqrt(-1) - Paolo P. Lava (ppl(AT)spl.at), Jun 09 2008
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CROSSREFS
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Recurrence in A100335, essentially a(n) differences.
Adjacent sequences: A137218 A137219 A137220 this_sequence A137222 A137223 A137224
Sequence in context: A034358 A036888 A053221 this_sequence A137234 A079094 A053220
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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 07 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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