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Search: id:A133407
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| A133407 |
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a(n)=a(n-1)+5*a(n-2) for n>=2, a(0)=1, a(1)=2 . |
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+0
1
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| 1, 2, 7, 17, 52, 137, 397, 1082, 3067, 8477, 23812, 66197, 185257, 516242, 1442527, 4023737, 11236372, 31355057, 87536917, 244312202, 681996787, 1903557797, 5313541732, 14831330717, 41399039377, 115555692962, 322550889847
(list; graph; listen)
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OFFSET
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0,2
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FORMULA
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G.f.: (1+x)/(1-x-5*x^2) .
a(n)=Sum_{k, 0<=k<=n+1}A122950(n+1,k)*4^(n+1-k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 08 2008
a(n)=(1/2)*[(1/2)+(1/2)*sqrt(21)]^n-(1/14)*sqrt(21)*[(1/2)-(1/2)*sqrt(21)]^n+(1/14)*[(1/2)+(1/2) *sqrt(21)]^n*sqrt(21)+(1/2)*[(1/2)-(1/2)*sqrt(21)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Nov 18 2008]
a(n)= ((21-3*sqrt(21))/42)*(0.5-0.5*sqrt(21))^n+((21+3*sqrt(21))/42)*(0.5+0.5*sqrt(21))^n [From Richard Choulet (richardchoulet(AT)yahoo.fr), Nov 20 2008]
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CROSSREFS
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Sequence in context: A014742 A085411 A007049 this_sequence A067602 A122382 A025554
Adjacent sequences: A133404 A133405 A133406 this_sequence A133408 A133409 A133410
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KEYWORD
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easy,nonn,new
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AUTHOR
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Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jan 03 2008
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