A017514 - OEIS

%I #22 Sep 08 2022 08:44:42

%S 1000000,85766121,1073741824,6321363049,24794911296,75418890625,

%T 192699928576,433626201009,885842380864,1677100110841,2985984000000,

%U 5053913144281,8198418170944,12827693806929,19456426971136

%N a(n) = (11*n + 10)^6.

%H G. C. Greubel, <a href="/A017514/b017514.txt">Table of n, a(n) for n = 0..1000</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(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(0)=1000000, a(1)=85766121, a(2)=1073741824, a(3)=6321363049, a(4)=24794911296, a(5)=75418890625, a(6)=192699928576. - _Harvey P. Dale_, Apr 21 2012

%F From _G. C. Greubel_, Oct 29 2019: (Start)

%F G.f.: (1000000 + 78766121*x + 494378977*x^2 + 571258822*x^3 + 127134022*x^4 + 2985977*x^5 + x^6)/(1-x)^7.

%F E.g.f.: (1000000 + 84766121*x + 451604791*x^2 + 559405990*x^3 + 233743565*x^4 + 36236475*x^5 + 1771561*x^6)*exp(x). (End)

%p seq((11*n+10)^6, n=0..20); # _G. C. Greubel_, Oct 29 2019

%t (11*Range[0,20]+10)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1}, {1000000, 85766121,1073741824,6321363049,24794911296, 75418890625, 192699928576},20] (* _Harvey P. Dale_, Apr 21 2012 *)

%o (Maxima) makelist((11*n+10)^6,n,0,30); /* _Martin Ettl_, Oct 21 2012 */

%o (PARI) vector(21, n, (11*n-1)^6) \\ _G. C. Greubel_, Oct 29 2019

%o (Magma) [(11*n+10)^6: n in [0..20]]; // _G. C. Greubel_, Oct 29 2019

%o (Sage) [(11*n+10)^6 for n in (0..20)] # _G. C. Greubel_, Oct 29 2019

%o (GAP) List([0..20], n-> (11*n+10)^6); # _G. C. Greubel_, Oct 29 2019

%Y Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), A017512 (m=4), A017513 (m=5), this sequence (m=6), A017515 (m=7), A017516 (m=8), A017517 (m=9), A017518 (m=10), A017519 (m=11), A017520 (m=12).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_