A329015 - OEIS

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A329015

a(n) = p(1,n), where p(x,n) is the strong divisibility sequence of polynomials based on sqrt(6) as in A327323.

1, 17, 229, 2873, 35101, 424337, 729667, 61370153, 736832461, 8843942657, 106137077509, 1273693758233, 15284569239421, 26202293082311, 2200998722429749, 26412015186735113, 316944334828711981, 3803332780883996897, 45639997185305228389, 547679985297149068793

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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..20.

EXAMPLE

See Example in A327323.

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[6]; 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}]]; (* A327323 *)

Table[f[x, n] /. x -> 0, {n, 1, 30}] (* A329014 *)

Table[f[x, n] /. x -> 1, {n, 1, 30}] (* A329015 *)

Table[f[x, n] /. x -> 2, {n, 1, 30}] (* A329016 *)

(* Peter J. C. Moses, Nov 01 2019 *)

CROSSREFS

Cf. A327323, A329014, A329016.

Sequence in context: A163853 A142547 A243229 * A016166 A358712 A206354

Adjacent sequences: A329012 A329013 A329014 * A329016 A329017 A329018

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 23 2019

STATUS

approved