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A329011
a(n) = p(0,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322.
3
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)).
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
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Nov 23 2019
STATUS
approved