A127989 - OEIS

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A127989

a(n) = 2*n^3 - 2*n + 9.

9, 21, 57, 129, 249, 429, 681, 1017, 1449, 1989, 2649, 3441, 4377, 5469, 6729, 8169, 9801, 11637, 13689, 15969, 18489, 21261, 24297, 27609, 31209, 35109, 39321, 43857, 48729, 53949, 59529, 65481, 71817, 78549, 85689, 93249, 101241, 109677, 118569

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OFFSET

1,1

COMMENTS

All numbers generated by the irreducible polynomial 2*n^3-2*n+9 are composite (indeed, they are multiples of 3). Largest prime factor A127990, smallest prime factor A127991, number of prime factors A127992.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

FORMULA

a(n) = 2*(n-1)*n*(n+1)+9 = 3*(2*A007290(n+1)+3).

G.f.: 3*x*(3-5*x+9*x^2-3*x^3)/(1-x)^4. - Bruno Berselli, Sep 09 2011

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Wesley Ivan Hurt, Oct 11 2021

MATHEMATICA

Table[2x^3 - 2x + 9, {x, 1, 100}]

LinearRecurrence[{4, -6, 4, -1}, {9, 21, 57, 129}, 50] (* G. C. Greubel, May 08 2018 *)

PROG

(Magma) [2*(n-1)*n*(n+1)+9: n in [1..50]]; // Vincenzo Librandi, Sep 13 2011