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a(n) = (11*n + 8)^6.
12

%I #26 Sep 08 2022 08:44:42

%S 262144,47045881,729000000,4750104241,19770609664,62523502209,

%T 164206490176,377149515625,782757789696,1500730351849,2699554153024,

%U 4608273662721,7529536000000,11853911588401,18075490334784,26808753332089,38806720086016,54980371265625

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

%H Vincenzo Librandi, <a href="/A017490/b017490.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F 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

%F a(n) = A001014(A017485(n)). - _Wesley Ivan Hurt_, May 21 2014

%F From _G. C. Greubel_, Sep 22 2019: (Start)

%F G.f.: (262144 +45210873*x +405183857*x^2 +625892702*x^3 +191449182*x^4 +7524433*x^5 +729*x^6)/(1-x)^7.

%F E.g.f.: (262144 +46783737*x +317585191*x^2 +450663290*x^3 +206511305*x^4 + 34303863*x^5 +1771561*x^6)*exp(x). (End)

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

%t (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 *)

%o (Magma) [(11*n+8)^6: n in [0..20]]; // _Vincenzo Librandi_, Sep 04 2011

%o (Maxima) makelist( (11*n+8)^6, n, 0, 20); /* _Martin Ettl_, Oct 21 2012 */

%o (PARI) vector(20, n, (11*n-3)^6) \\ _G. C. Greubel_, Sep 22 2019

%o (Sage) [(11*n+8)^6 for n in (0..20)] # _G. C. Greubel_, Sep 22 2019

%o (GAP) List([0..20], n-> (11*n+8)^6); # _G. C. Greubel_, Sep 22 2019

%Y 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).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_, Dec 11 1996