A329007 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(2) as in A327320.

1, 9, 21, 405, 2511, 5103, 92583, 557685, 372519, 20135709, 120873303, 241805655, 4353033231, 26119793709, 52241181741, 940355620245, 5642176768191, 3761465527701, 203119525916343, 1218718317759525, 2437437797780517, 43873890820402509, 263243376303474663

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 A327320.
		

Crossrefs

Cf. A327320, A329005, A329006.

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[2]; 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}]];  (* A327320 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329005 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329006 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329007 *)
(* Peter J. C. Moses, Nov 01 2019 *)