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Search: id:A090041
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| A090041 |
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a(n)=10a(n-1)-20a(n-2), a(0)=1, a(1)=6. |
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+0
3
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| 1, 6, 40, 280, 2000, 14400, 104000, 752000, 5440000, 39360000, 284800000, 2060800000, 14912000000, 107904000000, 780800000000, 5649920000000, 40883200000000, 295833600000000, 2140672000000000, 15490048000000000
(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.: (1-4x)/(1-10x+20x^2)=(1-4x)/((1-(5-sqrt(5))x)(1-(5+sqrt(5))x)); E.g.f. : exp(5x)(cosh(sqrt(5)x)+sinh(sqrt(5)x)/sqrt(5)); a(n)=((1+sqrt(5))(5+sqrt(5))^n-(1-sqrt(5))(5-sqrt(5))^n)/(2sqrt(5)).
Fifth binomial transform of (1, 1, 5, 5, 25, 25, ...) - Paul Barry (pbarry(AT)wit.ie), Nov 22 2003
3rd binomial transform of Fib(3n+1). - Paul Barry (pbarry(AT)wit.ie), Mar 23 2004
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CROSSREFS
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Cf. A090139.
Sequence in context: A081016 A083426 A122471 this_sequence A069720 A005037 A081337
Adjacent sequences: A090038 A090039 A090040 this_sequence A090042 A090043 A090044
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KEYWORD
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easy,nonn
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), Nov 20 2003
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