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Search: id:A080877
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| A080877 |
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a(n)*a(n+3) - a(n+1)*a(n+2) = 2^n, given a(0)=1, a(1)=1, a(2)=2. |
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+0
7
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| 1, 1, 2, 3, 8, 14, 40, 72, 208, 376, 1088, 1968, 5696, 10304, 29824, 53952, 156160, 282496, 817664, 1479168, 4281344, 7745024, 22417408, 40553472, 117379072, 212340736, 614604800, 1111830528, 3218112512, 5821620224, 16850255872
(list; graph; listen)
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OFFSET
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0,3
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FORMULA
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G.f.: (-3*x^3 - 4*x^2 + x + 1)/(4*x^4 - 6*x^2 + 1)
a(n + 4) = 6*a(n + 2) - 4*a(n) [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 06 2008]
a(n) = ( - 1/20*5^(1/2) + 1/16*5^(1/2)*2^(1/2) - 1/16*2^(1/2) + 1/4)*(sqrt(3 + sqrt(5)))^n + (1/20*5^(1/2) + 1/16*5^(1/2)*2^(1/2) + 1/16*2^(1/2) + 1/4)*(sqrt(3 - sqrt(5)))^n + ( - 1/20*5^(1/2) - 1/16*5^(1/2)*2^(1/2) + 1/16*2^(1/2) + 1/4)*( - (sqrt(3 + sqrt(5))))^n + (1/20*5^(1/2) - 1/16*5^(1/2)*2^(1/2) - 1/16*2^(1/2) + 1/4)*( - (sqrt(3 - sqrt(5))))^n [From Richard Choulet (richardchoulet(AT)yahoo.fr), Dec 07 2008]
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CROSSREFS
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Cf. A080876, A080878, A080879, A080880, A080881, A080882.
Cf. A154626, A098648 (bisections). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Oct 26 2009]
Sequence in context: A128305 A129700 A049344 this_sequence A007165 A107321 A005316
Adjacent sequences: A080874 A080875 A080876 this_sequence A080878 A080879 A080880
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KEYWORD
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nonn
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AUTHOR
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Paul D. Hanna (pauldhanna(AT)juno.com), Feb 22 2003
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