cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A017118 a(n) = (8*n + 4)^6.

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%I A017118 #19 Apr 25 2023 03:26:10
%S A017118 4096,2985984,64000000,481890304,2176782336,7256313856,19770609664,
%T A017118 46656000000,98867482624,192699928576,351298031616,606355001344,
%U A017118 1000000000000,1586874322944,2436396322816,3635215077376,5289852801024,7529536000000,10509215371264,14412774445056
%N A017118 a(n) = (8*n + 4)^6.
%H A017118 Vincenzo Librandi, <a href="/A017118/b017118.txt">Table of n, a(n) for n = 0..10000</a>
%H A017118 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F A017118 G.f.: -4096*(1 + 722*x + 10543*x^2 + 23548*x^3 + 10543*x^4 + 722*x^5 + x^6)/(x-1)^7. - _R. J. Mathar_, May 08 2015
%F A017118 From _Amiram Eldar_, Apr 25 2023: (Start)
%F A017118 a(n) = A017113(n)^6.
%F A017118 a(n) = 2^6*A016830(n) = 2^12*A016758(n).
%F A017118 Sum_{n>=0} 1/a(n) = Pi^6/3932160. (End)
%t A017118 (8*Range[0,30]+4)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{4096,2985984,64000000,481890304,2176782336,7256313856,19770609664},30] (* _Harvey P. Dale_, Jan 07 2016 *)
%o A017118 (Magma) [(8*n+4)^6: n in [0..20] ]; // _Vincenzo Librandi_, Jul 21 2011
%Y A017118 Cf. A016758, A016830, A017113.
%K A017118 nonn,easy
%O A017118 0,1
%A A017118 _N. J. A. Sloane_