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

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. A015518, A327321, A329009, A329010.

Programs

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 *)

Formula

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