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

1,2

Comments

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

Links

Table of n, a(n) for n=1..23.

Formula

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

Example

See Example in A327321.

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 *)

Crossrefs

Cf. A327321, A329008, A329010, A001511.

Sequence in context: A000854 A377382 A232517 * A110908 A232507 A336428

Adjacent sequences: A329006 A329007 A329008 * A329010 A329011 A329012

Keyword

nonn

Author

Clark Kimberling, Nov 08 2019

Status

approved