A017224 - OEIS

%I #25 Jan 11 2023 11:09:12

%S 625,38416,279841,1048576,2825761,6250000,12117361,21381376,35153041,

%T 54700816,81450625,116985856,163047361,221533456,294499921,384160000,

%U 492884401,623201296,777796321,959512576

%N a(n) = (9*n + 5)^4.

%H Vincenzo Librandi, <a href="/A017224/b017224.txt">Table of n, a(n) for n = 0..10000</a>

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

%F a(n) = A000583(A017221(n)).

%F From _Harvey P. Dale_, Apr 27 2016: (Start)

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).

%F G.f.: (625 + 35291*x + 94011*x^2 + 27281*x^3 + 256*x^4)/(1-x)^5. (End)

%F E.g.f.: (625 + 37791*x + 101817*x^2 + 53946*x^3 + 6561*x^4)*exp(x). - _G. C. Greubel_, Jan 06 2023

%t (9*Range[0,20]+5)^4 (* _Harvey P. Dale_, Apr 27 2016 *)

%o (Magma) [(9*n+5)^4: n in [0..35]] ; // _Vincenzo Librandi_, Jul 24 2011

%o (SageMath) [(9*n+5)^4 for n in range(41)] # _G. C. Greubel_, Jan 06 2023

%Y Sequences of the form (9*n+5)^k: A017221 (k=1), A017222 (k=2), A017223 (k=3), this sequence (k=4), A017225 (k=5), A017226 (k=6), A017227 (k=7), A017228 (k=8), A017229 (k=9), A017230 (k=10), A017231 (k=11).

%Y Cf. A000583 (n^4).

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_