A329014 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.

1, 5, 31, 185, 1111, 6665, 5713, 239945, 1439671, 8638025, 51828151, 310968905, 1865813431, 1599268655, 67169283511, 403015701065, 2418094206391, 14508565238345, 87051391430071, 522308348580425, 447692870211793, 18803100548895305, 112818603293371831

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 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, A329015, A329016.

Sequence in context: A255236 A202753 A057426 * A015540 A014987 A365741

Adjacent sequences: A329011 A329012 A329013 * A329015 A329016 A329017

Keyword

nonn,easy

Author

Clark Kimberling, Nov 23 2019

Status

approved