login
This site is supported by donations to The OEIS Foundation.

 

Logo

Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing.
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A123866 a(n) = n^6 - 1. 9
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) mod 7 = 0 iff n mod 7 > 0: a(A008589(n))=6; a(A047304(n)) = 0; a(n) mod 7 = 6*(1-A082784(n)).

a(n) = A005563(n-1)*A059826(n) = A068601(n)*A001093(n). - Reinhard Zumkeller, Feb 02 2007

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

FORMULA

G.f.: x^2*(63 + 287*x + 322*x^2 + 42*x^3 + 7*x^4 - x^5)/(1-x)^7. - Colin Barker, May 08 2012

a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(1)=0, a(2)=63, a(3)=728, a(4)=4095, a(5)=15624, a(6)=46655, a(7)=117648. - Harvey P. Dale, Nov 18 2012

Sum_{n>=2} 1/a(n) = 11/12 - Pi*sqrt(3)*tanh(Pi*sqrt(3)/2)/6. - Vaclav Kotesovec, Feb 14 2015

E.g.f.: 1 + (-1 + x + 31*x^2 + 90*x^3 + 65*x^4 + 15*x^5 + x^6)*exp(x). - G. C. Greubel, Aug 08 2019

MAPLE

A123866:=n->n^6 - 1; seq(A123866(n), n=1..40); # Wesley Ivan Hurt, Feb 26 2014

MATHEMATICA

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

LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 63, 728, 4095, 15624, 46655, 117648}, 30] (* Harvey P. Dale, Nov 18 2012 *)

PROG

(MAGMA) [n^6 - 1: n in [1..30]]; // Vincenzo Librandi, May 01 2011

(Maxima) A123866(n):=n^6 -1 $ makelist(A123866(n), n, 1, 30); /* Martin Ettl, Nov 05 2012 */

(Haskell)

a123866 = (subtract 1) . (^ 6)  -- Reinhard Zumkeller, Mar 11 2014

(PARI) a(n)=n^6-1 \\ Charles R Greathouse IV, Oct 07 2015

(Sage) [n^6 -1 for n in (1..30)] # G. C. Greubel, Aug 08 2019

(GAP) List([1..30], n-> n^6 -1); # G. C. Greubel, Aug 08 2019

CROSSREFS

Cf. A024004, A001014, A005563, A123865, A123867, A123868.

Sequence in context: A115152 A284953 A069091 * A024004 A284927 A321545

Adjacent sequences:  A123863 A123864 A123865 * A123867 A123868 A123869

KEYWORD

nonn,easy

AUTHOR

Reinhard Zumkeller, Oct 16 2006

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 12 07:00 EST 2019. Contains 329948 sequences. (Running on oeis4.)