A329013 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322.

1, 12, 147, 1836, 116721, 301644, 27679401, 52496748, 704739609, 47763633852, 1436395799961, 1798109838252, 323942200421841, 2430837436077972, 24315999958264707, 68401618078375404, 16418241358998948801, 13682794309260216588, 3694504558135555477881

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..19.

Example

See Example in A327322.

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[5]; 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}]];  (* A327322 *)
Table[f[x, n] /. x -> 0, {n, 1, 30}]   (* A329011 *)
Table[f[x, n] /. x -> 1, {n, 1, 30}]   (* A329012 *)
Table[f[x, n] /. x -> 2, {n, 1, 30}]   (* A329013 *)
(* Peter J. C. Moses, Nov 01 2019 *)

Crossrefs

Cf. A327320, A327321, A329011, A329012.

Sequence in context: A015501 A039493 A196454 * A350655 A167138 A001406

Adjacent sequences: A329010 A329011 A329012 * A329014 A329015 A329016

Keyword

nonn,easy

Author

Clark Kimberling, Nov 23 2019

Status

approved