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A329009
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a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
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3
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1, 4, 52, 80, 1936, 5824, 69952, 52480, 2519296, 7558144, 90698752, 136048640, 3265171456, 9795518464, 117546237952, 44079841280, 4231664828416, 12694994550784, 152339934871552, 228509902438400, 5484237659570176, 16452712979759104, 197432555761303552
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OFFSET
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1,2
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COMMENTS
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a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).
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LINKS
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FORMULA
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EXAMPLE
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MAPLE
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A329009 := n -> 2^(n - 1 - padic[ordp](2*n, 2))*(3^n - 1):
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MATHEMATICA
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c[poly_] := If[Head[poly] === Times, Times @@ DeleteCases[(#1 (Boole[MemberQ[#1, x] || MemberQ[#1, y] || MemberQ[#1, z]] &) /@Variables /@ #1 &)[List @@ poly], 0], poly];
r = Sqrt[3]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]]; (* A327321 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329008 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329009 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329010 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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