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Search: id:A122690
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| A122690 |
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a(0)=1, a(1)=4, a(n)=5*a(n-1)+4*a(n-2) for n>1. |
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+0
2
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| 1, 4, 24, 136, 776, 4424, 25224, 143816, 819976, 4675144, 26655624, 151978696, 866515976, 4940494664, 28168537224, 160604664776, 915697472776, 5220906022984, 29767320006024, 169720224122056, 967670400634376
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OFFSET
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0,2
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FORMULA
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a(n)=Sum_{k, 0<=k<=n} 4^k*A122542(n,k) . G.f. (1-x)/(1-5*x-4*x^2) . a(n+1)/a(n)-> (5+sqrt(41))/2 = 5.701562118716...if n-> infinity.
a(n)=(1/2)*[5/2-(1/2)*sqrt(41)]^n+(3/82)*sqrt(41)*[5/2+(1/2)*sqrt(41)]^n-(3/82)*sqrt(41)*[5/2-(1 /2)*sqrt(41)]^n+(1/2)*[5/2+(1/2)*sqrt(41)]^n, with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Jul 07 2008
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CROSSREFS
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Sequence in context: A057391 A071079 A153337 this_sequence A005319 A155119 A114169
Adjacent sequences: A122687 A122688 A122689 this_sequence A122691 A122692 A122693
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KEYWORD
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nonn
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Sep 22 2006
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
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