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A214731
a(n) = n^3 - 2*n^2 - 1.
2
-2, -1, 8, 31, 74, 143, 244, 383, 566, 799, 1088, 1439, 1858, 2351, 2924, 3583, 4334, 5183, 6136, 7199, 8378, 9679, 11108, 12671, 14374, 16223, 18224, 20383, 22706, 25199, 27868, 30719, 33758, 36991, 40424, 44063, 47914, 51983, 56276, 60799, 65558, 70559
OFFSET
1,1
FORMULA
From Bruno Berselli, Jul 27 2012: (Start)
G.f.: -x*(2-7*x-x^3)/(1-x)^4.
a(n) = A085490(n-1) + 2.
a(n) = A152619(n-2) - 1 for n>1.
a(n) - a(n-2) = A080859(n-2) - 1 for n>2. (End)
E.g.f.: 1 - (1-x)*(1+x)^2*exp(x). - G. C. Greubel, Dec 31 2023
MAPLE
A214731:=n->n^3-2*n^2-1: seq(A214731(n), n=1..60); # Wesley Ivan Hurt, Apr 18 2017
MATHEMATICA
Table[n^3 - 2 n^2 - 1, {n, 50}] (* Vincenzo Librandi, Jul 29 2012 *)
PROG
(PARI) a(n)=n^3-2*n^2-1 \\ Charles R Greathouse IV, Jul 27 2012
(Magma) [n^3-2*n^2-1: n in [1..50]]; // Vincenzo Librandi, Jul 29 2012
(SageMath) [n^2*(n-2)-1 for n in range(1, 51)] # G. C. Greubel, Dec 31 2023
CROSSREFS
Cf. A080859, A085490, A144390 (first differences), A152619.
Similar sequences: A152015 (of the type m^3+2m^2-1), A081437 (m^3-2m^2+1).
Sequence in context: A012965 A013119 A012962 * A079899 A333469 A239444
KEYWORD
sign,easy
AUTHOR
Marco Piazzalunga, Jul 27 2012
EXTENSIONS
a(3) corrected by Charles R Greathouse IV, Jul 27 2012
STATUS
approved