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Search: id:A096657
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| A096657 |
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a(n) = (2^n)*a(n-1) + (2^(n-1))*a(n-2), a(0)=1, a(1)=3. |
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3
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| 1, 3, 14, 124, 2096, 69056, 4486656, 578711552, 148724449280, 76295068188672, 78202296743231488, 160236429879963287552, 656488575092059763900416, 5378610735570941915498020864, 88128536246001466497105446043648
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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This is the sequence of numerators of self-convergents to the number 1.40861... whose self-continued fraction is (1,2,4,8,16,...)=A000079. See A096658 for denominators and A096654 for definitions.
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FORMULA
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a(n) is asymptotic to c*2^(n(n+1)/2) where c=2.1726687508496636560169136... - Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 02 2004
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EXAMPLE
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a(2)=4*3+2*1=14, a(3)=8*14+4*3=124.
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MATHEMATICA
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a[0] = 1; a[1] = 3; a[n_] := (2^n)*a[n-1] + (2^(n-1))*a[n-2]; Table[ a[n], {n, 0, 14}] (from Robert G. Wilson v Jul 03 2004)
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CROSSREFS
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Cf. A000079, A096654, A096658.
Sequence in context: A122081 A127850 A061029 this_sequence A126933 A073550 A002966
Adjacent sequences: A096654 A096655 A096656 this_sequence A096658 A096659 A096660
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling (ck6(AT)evansville.edu), Jul 01 2004
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EXTENSIONS
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More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jul 02 2004
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