A329017 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3/2) as in A328644.

1, 1, 7, 13, 11, 133, 463, 1261, 4039, 2321, 35839, 105469, 320503, 953317, 575267, 8596237, 25854247, 77431669, 232557151, 139429433, 2092490071, 6275373061, 18830313487, 56482551853, 6778577311, 508359743893, 1525146340543, 4575304803901, 13726182847159

Offset

1,3

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..29.

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, A329018, A329019.

Sequence in context: A115858 A114389 A259232 * A243389 A242584 A135555

Adjacent sequences: A329014 A329015 A329016 * A329018 A329019 A329020

Keyword

nonn

Author

Clark Kimberling, Nov 23 2019

Status

approved