A017512 - OEIS

%I #21 Sep 08 2022 08:44:42

%S 10000,194481,1048576,3418801,8503056,17850625,33362176,57289761,

%T 92236816,141158161,207360000,294499921,406586896,547981281,723394816,

%U 937890625,1196883216,1506138481,1871773696,2300257521,2798410000,3373402561,4032758016,4784350561

%N a(n) = (11*n + 10)^4.

%H G. C. Greubel, <a href="/A017512/b017512.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).

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

%F G.f.: (10000 + 144481*x + 176171*x^2 + 20731*x^3 + x^4)/(1-x)^5.

%F E.g.f.: (10000 + 184481*x + 334807*x^2 + 141086*x^3 + 14641*x^4)*exp(x). (End)

%p A017512:=n->(11*n+10)^4: seq(A017512(n), n=0..30); # _Wesley Ivan Hurt_, Apr 11 2017

%t (11*Range[0,30]+10)^4 (* or *) LinearRecurrence[{5,-10,10,-5,1}, {10000, 194481,1048576,3418801,8503056},30] (* _Harvey P. Dale_, Dec 24 2014 *)

%o (PARI) vector(31, n, (11*n-1)^4) \\ _G. C. Greubel_, Oct 29 2019

%o (Magma) [(11*n+10)^4: n in [0..30]]; // _G. C. Greubel_, Oct 29 2019

%o (Sage) [(11*n+10)^4 for n in (0..30)] # _G. C. Greubel_, Oct 29 2019

%o (GAP) List([0..30], n-> (11*n+10)^4); # _G. C. Greubel_, Oct 29 2019

%Y Powers of the form (11*n+10)^m: A017509 (m=1), A017510 (m=2), A017511 (m=3), this sequence (m=4), A017513 (m=5), A017514 (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_