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A329018 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.

%I A329018 #5 Dec 27 2019 16:35:49
%S A329018 1,7,43,259,311,9331,55987,335923,2015539,2418647,72559411,435356467,
%T A329018 2612138803,15672832819,18807399383,564221981491,3385331888947,
%U A329018 20311991333683,121871948002099,146246337602519,4387390128075571,26324340768453427,157946044610720563
%N A329018 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.
%C A329018 a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).
%e A329018 See Example in A328644.
%t A329018 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];
%t A329018 r = Sqrt[3/2]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
%t A329018 Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]];  (* A328644 *)
%t A329018 Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329017 *)
%t A329018 Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329018 *)
%t A329018 Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329019 *)
%t A329018 (* _Peter J. C. Moses_, Nov 01 2019 *)
%Y A329018 Cf. A328644, A329017, A329019.
%K A329018 nonn
%O A329018 1,2
%A A329018 _Clark Kimberling_, Nov 23 2019