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

1,2

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..18.

Example

See Example in A327323.

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 *)

Crossrefs

Cf. A327323, A329014, A329015.

Sequence in context: A006136 A199038 A182329 * A072080 A263515 A201245

Adjacent sequences: A329013 A329014 A329015 * A329017 A329018 A329019

Keyword

nonn,easy

Author

Clark Kimberling, Nov 23 2019

Status

approved