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Search: id:A111365
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| A111365 |
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a(n) = 5*a(n-1) + 3*a(n-2) where a(0) = a(1) = 1. |
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+0
1
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| 1, 1, 8, 43, 239, 1324, 7337, 40657, 225296, 1248451, 6918143, 38336068, 212434769, 1177182049, 6523214552, 36147618907, 200307738191, 1109981547676, 6150830952953, 34084099407793, 188872989897824, 1046617247712499
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OFFSET
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0,3
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REFERENCES
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Thomas Koshy, "Fibonacci and Lucas Numbers with Applications", Wiley, 2001
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FORMULA
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a(n)=(1/2)*[5/2-(1/2)*sqrt(37)]^n-(3/74)*[5/2+(1/2)*sqrt(37)]^n*sqrt(37)+(3/74)*[5/2-(1/2) *sqrt(37)]^n*sqrt(37)+(1/2)*[5/2+(1/2)*sqrt(37)]^n, with n>=0 [From Paolo P. Lava (ppl(AT)spl.at), Aug 01 2008]
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EXAMPLE
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a(2) = 5*a(1) + 3*a(0) = 5*1 + 3*1 = 8 which is the third term in the sequence.
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CROSSREFS
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Cf. A000045, A072264.
Sequence in context: A099253 A034361 A117617 this_sequence A144039 A044110 A044491
Adjacent sequences: A111362 A111363 A111364 this_sequence A111366 A111367 A111368
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KEYWORD
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nonn
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AUTHOR
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Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Nov 07 2005
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(at)rgwv.com), Nov 10 2005
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