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A060188
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A column and diagonal of A060187.
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8
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1, 6, 23, 76, 237, 722, 2179, 6552, 19673, 59038, 177135, 531428, 1594309, 4782954, 14348891, 43046704, 129140145, 387420470, 1162261447, 3486784380, 10460353181, 31381059586, 94143178803, 282429536456, 847288609417
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OFFSET
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2,2
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COMMENTS
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Sums of rows of the numerators and of the denominators of the redundant Stern-Brocot structure A152975/A152976: a(n+2) = Sum_{k=2^n..(2^(n+1) -1)} A152975(k) = Sum_{k=2^n..(2^(n+1) -1)} A152976(k). - Reinhard Zumkeller, Dec 22 2008
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LINKS
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P. A. MacMahon, The divisors of numbers, Proc. London Math. Soc., (2) 19 (1920), 305-340; Coll. Papers II, pp. 267-302.
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FORMULA
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With offset 0, this is 3^(n+1) - n - 2.
a(n) = 5*a(n-1) - 7*a(n-2) + 3*a(n-3).
G.f.: x^2*(1 + x)/((1-x)^2*(1-3*x)). (End)
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MAPLE
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a[0]:=1:for n from 1 to 24 do a[n]:=(4*a[n-1]-3*a[n-2]+2) od: seq(a[n], n=0..24); # Zerinvary Lajos, Jun 08 2007
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MATHEMATICA
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PROG
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(Sage) [3^(n-1) -n for n in (2..32)] # G. C. Greubel, Jan 07 2022
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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