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.

1, 7, 43, 259, 311, 9331, 55987, 335923, 2015539, 2418647, 72559411, 435356467, 2612138803, 15672832819, 18807399383, 564221981491, 3385331888947, 20311991333683, 121871948002099, 146246337602519, 4387390128075571, 26324340768453427, 157946044610720563

Offset: 1

Author

Clark Kimberling, Nov 23 2019

Keywords

• nonn

Comments

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

Examples

			See Example in A328644.
		

Crossrefs

Cf. A328644, A329017, A329019.

Programs

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[3/2]; 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}]];  (* A328644 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329017 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329018 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329019 *)
(* Peter J. C. Moses, Nov 01 2019 *)