A255877 a(n) = (2n-2)^3 + (2n-2) - 1.

-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

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 *)

Prog

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

Crossrefs

Sequence in context: A231199 A354532 A332456 * A197277 A238317 A105287

Adjacent sequences: A255874 A255875 A255876 * A255878 A255879 A255880

Keyword

sign,easy

Author

Arka Mal, Mar 08 2015

Extensions

More terms from Vincenzo Librandi, Mar 17 2015

Status

approved