A329009 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.

1, 4, 52, 80, 1936, 5824, 69952, 52480, 2519296, 7558144, 90698752, 136048640, 3265171456, 9795518464, 117546237952, 44079841280, 4231664828416, 12694994550784, 152339934871552, 228509902438400, 5484237659570176, 16452712979759104, 197432555761303552

Offset: 1

Author

Clark Kimberling, Nov 08 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 A327321.
		

Crossrefs

Cf. A327321, A329008, A329010, A001511.

Programs

Maple

A329009 := n -> 2^(n - 1 - padic[ordp](2*n, 2))*(3^n - 1):
seq(A329009(n), n = 1..22);  # Peter Luschny, Mar 05 2022

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 *)

Formula

a(n) = 2^(n - 1 - A001511(n))*(3^n - 1). - Peter Luschny, Mar 05 2022