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.

A017331 a(n) = (10*n + 5)^3.

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%I A017331 #27 Aug 23 2024 11:59:37
%S A017331 125,3375,15625,42875,91125,166375,274625,421875,614125,857375,
%T A017331 1157625,1520875,1953125,2460375,3048625,3723875,4492125,5359375,
%U A017331 6331625,7414875,8615125,9938375,11390625,12977875,14706125,16581375,18609625,20796875,23149125,25672375
%N A017331 a(n) = (10*n + 5)^3.
%H A017331 Vincenzo Librandi, <a href="/A017331/b017331.txt">Table of n, a(n) for n = 0..10000</a>
%H A017331 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A017331 G.f.: 125*(x+1)*(x^2 + 22*x + 1)/(x-1)^4. - _Colin Barker_, Nov 14 2012
%F A017331 From _Amiram Eldar_, Apr 18 2023: (Start)
%F A017331 a(n) = A017329(n)^3.
%F A017331 a(n) = 5^3 * A016755(n).
%F A017331 Sum_{n>=0} 1/a(n) = 7*zeta(3)/1000.
%F A017331 Sum_{n>=0} (-1)^n/a(n) = Pi^3/4000. (End)
%t A017331 Table[(10*n + 5)^3, {n, 0, 30}] (* _Amiram Eldar_, Apr 18 2023 *)
%t A017331 LinearRecurrence[{4,-6,4,-1},{125,3375,15625,42875},30] (* _Harvey P. Dale_, Aug 23 2024 *)
%o A017331 (Magma) [(10*n+5)^3: n in [0..35]]; // _Vincenzo Librandi_, Aug 02 2011
%o A017331 (PARI) a(n)=(10*n+5)^3 \\ _Charles R Greathouse IV_, Aug 02 2011
%Y A017331 Cf. A002117, A016755, A017329.
%K A017331 nonn,easy
%O A017331 0,1
%A A017331 _N. J. A. Sloane_