A329016 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.

1, 29, 643, 12905, 246931, 4605809, 12096589, 1543657385, 28000191811, 506361400289, 9140442629803, 164813279007065, 2969777450503891, 7641502403030567, 963209052615434683, 17341940195247239945, 312200873244313891171, 5620121165426149334849

Offset: 1

Author

Clark Kimberling, Nov 23 2019

Keywords

• nonn
• easy

Comments

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

Examples

			See Example in A327323.
		

Crossrefs

Cf. A327323, A329014, A329015.

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[6]; 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}]];  (* A327323 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329014 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329015 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329016 *)
(* Peter J. C. Moses, Nov 01 2019 *)