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A329013 a(n) = p(2,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(5) as in A327322. 3
1, 12, 147, 1836, 116721, 301644, 27679401, 52496748, 704739609, 47763633852, 1436395799961, 1798109838252, 323942200421841, 2430837436077972, 24315999958264707, 68401618078375404, 16418241358998948801, 13682794309260216588, 3694504558135555477881 (list; graph; refs; listen; history; text; internal format)
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 * A167138 A001406 A057572

Adjacent sequences:  A329010 A329011 A329012 * A329014 A329015 A329016

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 23 2019

STATUS

approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)