A024004 a(n) = 1 - n^6.

1, 0, -63, -728, -4095, -15624, -46655, -117648, -262143, -531440, -999999, -1771560, -2985983, -4826808, -7529535, -11390624, -16777215, -24137568, -34012223, -47045880, -63999999, -85766120, -113379903, -148035888, -191102975, -244140624, -308915775, -387420488, -481890303

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Formula

From G. C. Greubel, May 11 2017: (Start)

G.f.: (1 - 7*x - 42*x^2 - 322*x^3 - 287*x^4 - 63*x^5)/(1 - x)^7.

E.g.f.: (1 - x - 31*x^2 - 90*x^3 - 65*x^4 - 15*x^5 - x^6)*exp(x). (End)

Sum_{k>=2} -1/a(k) = 11/12 - Pi*tanh(sqrt(3)*Pi/2)/(2*sqrt(3)) = A339529. - Vaclav Kotesovec, Dec 08 2020

Mathematica

Table[1-n^6, {n, 0, 40}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *)

Prog

(Magma) [1-n^6: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
(Maxima) A024004(n):=1-n^6 $ makelist(A024004(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(Haskell)
a024004 = (1 -) . (^ 6)  -- Reinhard Zumkeller, Mar 11 2014
(PARI) for(n=0, 50, print1(1-n^6, ", ")) \\ G. C. Greubel, May 11 2017

Crossrefs

Cf. A001014.

a(n) = -A123866(n) for n > 0.

Sequence in context: A284953 A069091 A123866 * A284927 A321545 A201886

Adjacent sequences: A024001 A024002 A024003 * A024005 A024006 A024007

Keyword

sign,easy

Author

N. J. A. Sloane, corrected Mar 01 2007

Status

approved