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A329008
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a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
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4
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1, 1, 7, 5, 61, 91, 547, 205, 4921, 7381, 44287, 33215, 398581, 597871, 3587227, 672605, 32285041, 48427561, 290565367, 217924025, 2615088301, 3922632451, 23535794707, 8825923015, 211822152361, 317733228541, 1906399371247, 1429799528435, 17157594341221
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OFFSET
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1,3
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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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Table of n, a(n) for n=1..29.
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FORMULA
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a(2*n - 1) = A015518(2*n - 1). - Vaclav Kotesovec, Mar 19 2022
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EXAMPLE
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See Example in A327321.
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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 *)
(* Peter J. C. Moses, Nov 01 2019 *)
Numerator[CoefficientList[Normal[Series[1/((4 + x)*(4 - 3*x)), {x, 0, 30}]], x]] (* Vaclav Kotesovec, Mar 19 2022 *)
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CROSSREFS
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Cf. A015518, A327321, A329009, A329010.
Sequence in context: A089244 A063003 A038271 * A005692 A080798 A007553
Adjacent sequences: A329005 A329006 A329007 * A329009 A329010 A329011
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Nov 08 2019
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STATUS
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approved
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