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

1,2

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..23.

Example

See Example in A327320.

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 *)

Crossrefs

Cf. A327320, A329005, A329006.

Sequence in context: A339724 A342409 A373747 * A368120 A250729 A251292

Adjacent sequences: A329004 A329005 A329006 * A329008 A329009 A329010

Keyword

nonn

Author

Clark Kimberling, Nov 08 2019

Status

approved