A329008 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.

1, 1, 7, 5, 61, 91, 547, 205, 4921, 7381, 44287, 33215, 398581, 597871, 3587227, 672605, 32285041, 48427561, 290565367, 217924025, 2615088301, 3922632451, 23535794707, 8825923015, 211822152361, 317733228541, 1906399371247, 1429799528435, 17157594341221

Offset

1,3

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..29.

Formula

a(2*n - 1) = A015518(2*n - 1). - Vaclav Kotesovec, Mar 19 2022

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 *)
Numerator[CoefficientList[Normal[Series[1/((4 + x)*(4 - 3*x)), {x, 0, 30}]], x]] (* Vaclav Kotesovec, Mar 19 2022 *)

Crossrefs

Cf. A015518, A327321, A329009, A329010.

Sequence in context: A089244 A063003 A038271 * A005692 A080798 A007553

Adjacent sequences: A329005 A329006 A329007 * A329009 A329010 A329011

Keyword

nonn

Author

Clark Kimberling, Nov 08 2019

Status

approved