A329011 a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322.

1, 2, 7, 26, 521, 434, 13021, 8138, 36169, 813802, 8138021, 3390842, 203450521, 508626302, 1695421007, 1589457194, 127156575521, 35321270978, 3178914388021, 3973642985026, 26490953233507, 198682149251302, 1986821492513021, 413921144273546, 49670537312825521

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..25.

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, A329012, A329013.

Sequence in context: A005519 A290305 A343595 * A037381 A129013 A150591

Adjacent sequences: A329008 A329009 A329010 * A329012 A329013 A329014

Keyword

nonn,easy

Author

Clark Kimberling, Nov 23 2019

Status

approved