login
a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322.
3

%I #5 Dec 07 2019 01:44:08

%S 1,12,147,1836,116721,301644,27679401,52496748,704739609,47763633852,

%T 1436395799961,1798109838252,323942200421841,2430837436077972,

%U 24315999958264707,68401618078375404,16418241358998948801,13682794309260216588,3694504558135555477881

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

%C a(n) is a strong divisibility sequence; i.e., gcd(a(h),a(k)) = a(gcd(h,k)).

%e See Example in A327322.

%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[5]; 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}]]; (* A327322 *)

%t Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329011 *)

%t Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329012 *)

%t Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329013 *)

%t (* _Peter J. C. Moses_, Nov 01 2019 *)

%Y Cf. A327320, A327321, A329011, A329012.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Nov 23 2019