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a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.
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%I #5 Dec 27 2019 16:36:02

%S 1,13,133,1261,2321,105469,953317,8596237,77431669,139429433,

%T 6275373061,56482551853,508359743893,4575304803901,8235602334113,

%U 370603178776909,3335432903959477,30018913315504477,270170288559017029,486306574381812041,21883796946693169621

%N 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 a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).

%e See Example in A328644.

%t 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 r = Sqrt[3/2]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];

%t Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]]; (* A328644 *)

%t Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329017 *)

%t Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329018 *)

%t Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329019 *)

%t (* _Peter J. C. Moses_, Nov 01 2019 *)

%Y Cf. A328644, A329017, A329018.

%K nonn

%O 1,2

%A _Clark Kimberling_, Nov 23 2019