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 A329008 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321. 4
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)). LINKS FORMULA a(2*n - 1) = A015518(2*n - 1). - Vaclav Kotesovec, Mar 19 2022 EXAMPLE See Example in A327321. MATHEMATICA 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 *) CROSSREFS Cf. A015518, A327321, A329009, A329010. Sequence in context: A089244 A063003 A038271 * A005692 A080798 A007553 Adjacent sequences: A329005 A329006 A329007 * A329009 A329010 A329011 KEYWORD nonn AUTHOR Clark Kimberling, Nov 08 2019 STATUS approved

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Last modified February 7 12:44 EST 2023. Contains 360123 sequences. (Running on oeis4.)