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A152046
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a(n) = Product_{k=1..floor((n-1)/2)} (1 + 8*cos(k*Pi/n)^2) for n >= 0.
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6
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1, 1, 1, 3, 5, 11, 21, 43, 85, 171, 341, 683, 1365, 2731, 5461, 10923, 21845, 43691, 87381, 174763, 349525, 699051, 1398101, 2796203, 5592405, 11184811, 22369621, 44739243, 89478485, 178956971, 357913941, 715827883, 1431655765, 2863311531, 5726623061, 11453246123
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OFFSET
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0,4
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COMMENTS
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LINKS
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FORMULA
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G.f.: 1 + A(x) where A(x) is the g.f. of A001045.
G.f.: 1 + Q(0)/3, where Q(k)= 1 - 1/(4^k - 2*x*16^k/(2*x*4^k - 1/(1 + 1/(2*4^k - 8*x*16^k/(4*x*4^k + 1/Q(k+1)))))); (continued fraction).
G.f.: 1+ Q(0)*x/2 , where Q(k) = 1 + 1/(1 - x*(2*k+1 + 2*x)/( x*(2*k+2 + 2*x) + 1/Q(k+1) )); (continued fraction). (End)
a(n) = a(n-1) + 2*a(n-2) for n>2.
a(n) = ((-1)^(1 + n) + 2^n)/ 3 for n>0. (End)
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MATHEMATICA
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a[n_] := Product[(1 + 8 Cos[k Pi/n]^2), {k, 1, Floor[(n - 1)/2]}];
Table[Round[a[n]], {n, 0, 20}]
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PROG
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(PARI) Vec((1 - 2*x^2) / ((1 + x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, Nov 28 2019
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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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