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A329009 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321. 3
1, 4, 52, 80, 1936, 5824, 69952, 52480, 2519296, 7558144, 90698752, 136048640, 3265171456, 9795518464, 117546237952, 44079841280, 4231664828416, 12694994550784, 152339934871552, 228509902438400, 5484237659570176, 16452712979759104, 197432555761303552 (list; graph; refs; listen; history; text; internal format)
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: A182044 A000854 A232517 * A110908 A232507 A336428

Adjacent sequences: A329006 A329007 A329008 * A329010 A329011 A329012

KEYWORD

nonn

AUTHOR

Clark Kimberling, Nov 08 2019

STATUS

approved

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Last modified February 6 04:21 EST 2023. Contains 360097 sequences. (Running on oeis4.)