A121671 - OEIS

%I #29 Apr 09 2024 17:20:41

%S 1,-4,41,316,1121,2876,6121,11516,19841,31996,49001,71996,102241,

%T 141116,190121,250876,325121,414716,521641,647996,796001,967996,

%U 1166441,1393916,1653121,1946876,2278121,2649916,3065441,3527996,4041001,4607996,5232641,5918716

%N Real part of (1 + n*i)^5.

%C The imaginary term considered as an unsigned real integer = A121672(n). The companion sequence A121672 uses the operation (n + i)^5.

%H Vincenzo Librandi, <a href="/A121671/b121671.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 G.f.: (1-9*x+71*x^2+61*x^3-4*x^4)/(1-x)^5. - _Bruno Berselli_, Mar 01 2012

%F a(n) = 5*n^4-10*n^2+1. - _Bruno Berselli_, Mar 01 2012

%F a(n) = (1+n^2)^(5/2)*cos(5*arctan(n)). - _Gerry Martens_, Apr 06 2024

%e a(4) = 1121 since (1 + 4i)^5 = (1121 + 404i) where 404 = A121672(4).

%t Table[Re[(1 + n*I)^5], {n, 0, 35}] (* _T. D. Noe_, Mar 01 2012 *)

%t LinearRecurrence[{5,-10,10,-5,1},{1,-4,41,316,1121},40] (* _Harvey P. Dale_, Apr 21 2019 *)

%o (PARI) a(n) = real((1 + n*I)^5); \\ _Michel Marcus_, Dec 19 2020

%Y Cf. A121672.

%K sign,easy

%O 0,2

%A _Gary W. Adamson_, Aug 14 2006

%E Corrected and extended by _T. D. Noe_, Mar 01 2012