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Search: id:A104487
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| A104487 |
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a(n+3) = 6a(n+2) - 10a(n+1) + 3a(n); a(0) = 1, a(1) = 4, a(2) = 14. |
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+0
1
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| 1, 4, 14, 47, 154, 496, 1577, 4964, 15502, 48103, 148490, 456416, 1397905, 4268740, 13002638, 39522143, 119912698, 363262672, 1099015481, 3321204260, 10026858766, 30246156439, 91171963754, 274650794432, 826923598369
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Binomial transform of A104004.
If another a(0)=0 is added in front, also the binomial transform of A027934.
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FORMULA
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G.f. (2*x-1)/((3*x-1)*(x^2-3*x+1)) Define c = (3+sqrt(5))/2 and d = (3-sqrt(5))/2. Then a(n) = 3^(n+1) - ((2*sqrt(5)/5)+1)*c^n + ((2*sqrt(5)/5)-1)*d^n
3^(n+1) - Fibonacci(2n+3). - Ralf Stephan, May 20 2007
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CROSSREFS
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Sequence in context: A121530 A121299 A046718 this_sequence A094789 A082574 A137284
Adjacent sequences: A104484 A104485 A104486 this_sequence A104488 A104489 A104490
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KEYWORD
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nonn
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AUTHOR
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Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Apr 19 2005
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EXTENSIONS
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Corrected comment concerning the binomial transforms - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 26 2009
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