|
%I #6 Nov 23 2019 13:40:59
%S 1,7,151,371,13981,64477,1176211,1333003,96366841,434627347,
%T 7833057871,17636587241,635161281301,2858836117417,51465153629131,
%U 28951056265019,4169104690053361,18761352574966687,337708161046665991,759848130726580511,27354628073588539021
%N a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(3) as in A327321.
%C a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).
%e See Example in A327321.
%t 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];
%t r = Sqrt[3]; f[x_, n_] := c[Factor[Expand[(r x + r)^n - (r x - 1/r)^n]]];
%t Flatten[Table[CoefficientList[f[x, n], x], {n, 1, 12}]]; (* A327321 *)
%t Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329008 *)
%t Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329009 *)
%t Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329010 *)
%t (* _Peter J. C. Moses_, Nov 01 2019 *)
%Y Cf. A327321, A329008, A329009.
%K nonn
%O 1,2
%A _Clark Kimberling_, Nov 08 2019
|
