A017490 a(n) = (11*n + 8)^6.

262144, 47045881, 729000000, 4750104241, 19770609664, 62523502209, 164206490176, 377149515625, 782757789696, 1500730351849, 2699554153024, 4608273662721, 7529536000000, 11853911588401, 18075490334784, 26808753332089, 38806720086016, 54980371265625

Offset: 0

Author

N. J. A. Sloane, Dec 11 1996

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).

Crossrefs

Powers of the form (11*n+8)^m: A017485 (m=1), A017486 (m=2), A017487 (m=3), A017488 (m=4), A017489 (m=5), this sequence (m=6), A017491 (m=7), A017492 (m=8), A017493 (m=9), A017494 (m=10), A017495 (m=11), A017496 (m=12).

Programs

GAP

List([0..20], n-> (11*n+8)^6); # G. C. Greubel, Sep 22 2019

Magma

[(11*n+8)^6: n in [0..20]]; // Vincenzo Librandi, Sep 04 2011

Maple

A017490:=n->(11*n+8)^6; seq(A017490(n), n=0..20); # Wesley Ivan Hurt, May 21 2014

Mathematica

(11*Range[0,20]+8)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {262144, 47045881, 729000000, 4750104241, 19770609664, 62523502209, 164206490176}, 20] (* Harvey P. Dale, Nov 08 2013 *)

Maxima

makelist( (11*n+8)^6, n, 0, 20); /* Martin Ettl, Oct 21 2012 */

PARI

vector(20, n, (11*n-3)^6) \\ G. C. Greubel, Sep 22 2019

Sage

[(11*n+8)^6 for n in (0..20)] # G. C. Greubel, Sep 22 2019

Formula

a(0)=262144, a(1)=47045881, a(2)=729000000, a(3)=4750104241, a(4)=19770609664, a(5)=62523502209, a(6)=164206490176, 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). - Harvey P. Dale, Nov 08 2013

a(n) = A001014(A017485(n)). - Wesley Ivan Hurt, May 21 2014

From G. C. Greubel, Sep 22 2019: (Start)

G.f.: (262144 [phone]*x [phone]*x^2 [phone]*x^3 [phone]*x^4 +7524433*x^5 +729*x^6)/(1-x)^7.

E.g.f.: (262144 [phone]*x [phone]*x^2 [phone]*x^3 [phone]*x^4 + 34303863*x^5 +1771561*x^6)*exp(x). (End)