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A329013
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a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322.
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3
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1, 12, 147, 1836, 116721, 301644, 27679401, 52496748, 704739609, 47763633852, 1436395799961, 1798109838252, 323942200421841, 2430837436077972, 24315999958264707, 68401618078375404, 16418241358998948801, 13682794309260216588, 3694504558135555477881
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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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EXAMPLE
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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[5]; 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}]]; (* A327322 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329011 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329012 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329013 *)
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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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STATUS
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approved
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