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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
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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; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Binomial transform of A104004.
If another a(0)=0 is added in front, also the binomial transform of A027934.
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FORMULA
| 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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PROG
| (MAGMA) [3^(n+1) - Fibonacci(2*n+3): n in [0..30]]; // Vincenzo Librandi, Apr 21 2011
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CROSSREFS
| Sequence in context: A121299 A046718 A192877 * A094789 A082574 A137284
Adjacent sequences: A104484 A104485 A104486 * A104488 A104489 A104490
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KEYWORD
| nonn
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AUTHOR
| Creighton Dement (creighton.k.dement(AT)uni-oldenburg.de), Apr 19 2005
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EXTENSIONS
| Corrected comment concerning the binomial transforms - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 26 2009
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