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Search: id:A133654
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| 1, 3, 9, 23, 57, 139, 337, 815, 1969, 4755, 11481, 27719, 66921, 161563, 390049, 941663, 2273377, 5488419, 13250217, 31988855, 77227929, 186444715, 450117361, 1086679439, 2623476241, 6333631923, 15290740089, 89120964297
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OFFSET
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1,2
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COMMENT
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a(n)/a(n-1) tends to (1 + sqrt(2)).
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FORMULA
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a(n) = 2*A000129(n) - 1; where A000129 = the Pell sequence, (1, 2, 5, 12, 29,...). a(1) = 1, a(2) = 3, then for n>2, a(n) = 2*a(n-1) + a(n-2) + 2.
G.f.: x*(1+x^2)/(-1+x)/(-1+2*x+x^2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Nov 14 2007
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EXAMPLE
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a(3) = 2*A000129(3) - 1 = 2*5 - 1.
a(5) = 57 = 2*a(4) + a(3) + 2 = 2*23 + 9 + 2.
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CROSSREFS
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Cf. A000129.
Sequence in context: A147126 A147212 A045883 this_sequence A096574 A045650 A077847
Adjacent sequences: A133651 A133652 A133653 this_sequence A133655 A133656 A133657
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Sep 19 2007
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EXTENSIONS
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More terms from Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 16 2007
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