A329019 a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.

1, 13, 133, 1261, 2321, 105469, 953317, 8596237, 77431669, 139429433, 6275373061, 56482551853, 508359743893, 4575304803901, 8235602334113, 370603178776909, 3335432903959477, 30018913315504477, 270170288559017029, 486306574381812041, 21883796946693169621

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..21.

Example

See Example in A328644.

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[3/2]; 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}]];  (* A328644 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329017 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329018 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329019 *)
(* Peter J. C. Moses, Nov 01 2019 *)

Crossrefs

Cf. A328644, A329017, A329018.

Sequence in context: A198664 A332243 A081042 * A016153 A187732 A031138

Adjacent sequences: A329016 A329017 A329018 * A329020 A329021 A329022

Keyword

nonn

Author

Clark Kimberling, Nov 23 2019

Status

approved