A329010 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.

1, 7, 151, 371, 13981, 64477, 1176211, 1333003, 96366841, 434627347, 7833057871, 17636587241, 635161281301, 2858836117417, 51465153629131, 28951056265019, 4169104690053361, 18761352574966687, 337708161046665991, 759848130726580511, 27354628073588539021

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..21.

Example

See Example in A327321.

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, A329009.

Sequence in context: A229806 A229880 A070248 * A309855 A364845 A339582

Adjacent sequences: A329007 A329008 A329009 * A329011 A329012 A329013

Keyword

nonn

Author

Clark Kimberling, Nov 08 2019

Status

approved