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A255877 a(n) = (2n-2)^3 +(2n-2) - 1. 0
-1, 9, 67, 221, 519, 1009, 1739, 2757, 4111, 5849, 8019, 10669, 13847, 17601, 21979, 27029, 32799, 39337, 46691, 54909, 64039, 74129, 85227, 97381, 110639, 125049, 140659, 157517, 175671, 195169, 216059, 238389, 262207, 287561, 314499, 343069, 373319 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)/a(n-1) tends to 1 as n becomes very large (of order 10^3 or more).

LINKS

Table of n, a(n) for n=1..37.

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

FORMULA

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

G.f.: x*(-1 + 13*x + 25*x^2 + 11*x^3)/(1-x)^4. - Vincenzo Librandi, Mar 17 2015

a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4) for n>4. - Vincenzo Librandi, Mar 17 2015

EXAMPLE

a(3) = (2*3-2)^3 + (2*3-2) - 1 = 67.

MATHEMATICA

Table[(2 n - 2)^3 + (2 n - 2) - 1, {n, 30}] (* Michael De Vlieger, Mar 17 2015 *)

CoefficientList[Series[(-1 + 13 x + 25 x^2 + 11 x^3) / (1 - x)^4, {x, 0, 40}], x] (* Vincenzo Librandi, Mar 17 2015 *)

PROG

(JAVA)

class Generator

{   //function to generate n-th number of the sequence

    public int generate(int n)

    {

        return (int)(Math.pow((2*n-2), 3))+(2*n-2)-1;

    }

}

(MAGMA) [(2*n-2)^3 +(2*n-2) - 1: n in [1..40]] /* or */ I:=[-1, 9, 67, 221]; [n le 4 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..40]]; // Vincenzo Librandi, Mar 17 2015

(PARI) a(n)=8*n^3 - 24*n^2 + 26*n - 11 \\ Charles R Greathouse IV, Mar 17 2015

CROSSREFS

Sequence in context: A232018 A231199 A332456 * A197277 A238317 A105287

Adjacent sequences:  A255874 A255875 A255876 * A255878 A255879 A255880

KEYWORD

sign,easy,hear

AUTHOR

Arka Mal, Mar 08 2015

EXTENSIONS

More terms from Vincenzo Librandi, Mar 17 2015

STATUS

approved

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Last modified September 26 19:00 EDT 2021. Contains 347670 sequences. (Running on oeis4.)