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A173989
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a(n) is the 2-adic valuation of A173300(n).
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2
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0, 0, 1, 1, 2, 1, 3, 3, 4, 3, 5, 5, 6, 5, 7, 7, 8, 7, 9, 9, 10, 9, 11, 11, 12, 11, 13, 13, 14, 13, 15, 15, 16, 15, 17, 17, 18, 17, 19, 19, 20, 19, 21, 21, 22, 21, 23, 23, 24, 23, 25, 25, 26, 25, 27, 27, 28, 27, 29, 29, 30, 29, 31, 31, 32, 31, 33, 33, 34, 33, 35, 35, 36, 35, 37, 37, 38, 37
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OFFSET
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1,5
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COMMENTS
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Conjecture: always follows the pattern A, A, A+1, A, where A is an odd number.
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LINKS
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FORMULA
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G.f.: x^3*(1 + x^2 - x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
a(n) = a(n-1) + a(n-4) - a(n-5) for n > 7.
(End)
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MAPLE
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A173300 := proc(n) local x, y ; x := (1+sqrt(3))/2 ; y := (1-sqrt(3))/2 ; denom(expand(x^n+y^n)) ; end proc:
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MATHEMATICA
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Log2[Denominator[Map[First, NestList[{Last[#], Last[#] + First[#]/2} &, {1, 2}, 100]]]] (* Paolo Xausa, Feb 01 2024, after Nick Hobson in A173300 *)
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PROG
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A173300(n) = denominator(2*polcoeff( lift( Mod((1+x)/2, x^2-3)^n ), 0))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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