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A259821
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a(n) = floor( (3^n+1)^2/3^n ).
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1
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4, 5, 11, 29, 83, 245, 731, 2189, 6563, 19685, 59051, 177149, 531443, 1594325, 4782971, 14348909, 43046723, 129140165, 387420491, 1162261469, 3486784403, 10460353205, 31381059611, 94143178829, 282429536483
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OFFSET
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0,1
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COMMENTS
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a(n) is the curvature (rounded down) of circles inscribed between a unit circle and a circumscribed equilateral triangle. See illustration.
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LINKS
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FORMULA
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a(n) = 3^n + 2 for n>0.
a(n) = 4*a(n-1) - 3*a(n-2) for n>2.
G.f.: (3*x^2-11*x+4) / ((x-1)*(3*x-1)).
(End)
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MATHEMATICA
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PROG
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(PARI)
a(n)=floor((3^n+1)^2/3^n)
for (n=0, 100, print1(a(n), ", "))
(PARI) Vec((3*x^2-11*x+4)/((x-1)*(3*x-1)) + O(x^100)) \\ Colin Barker, Jul 07 2015
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CROSSREFS
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KEYWORD
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nonn,easy,less
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AUTHOR
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STATUS
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approved
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