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.
%I A022521 #68 May 13 2023 13:36:58
%S A022521 1,31,211,781,2101,4651,9031,15961,26281,40951,61051,87781,122461,
%T A022521 166531,221551,289201,371281,469711,586531,723901,884101,1069531,
%U A022521 1282711,1526281,1803001,2115751,2467531
%N A022521 a(n) = (n+1)^5 - n^5.
%C A022521 Last digit of a(n) is always 1. Last two digits of a(n) (i.e., a(n) mod 100) are repeated periodically with palindromic part of period 20 {1,31,11,81,1,51,31,61,81,51,51,81,61,31,51,1,81,11,31,1}. Last three digits of a(n) (i.e., a(n) mod 1000) are repeated periodically with palindromic part of period 200. - _Alexander Adamchuk_, Aug 11 2006
%C A022521 In Conway and Guy, these numbers are called nexus numbers of order 5. - _M. F. Hasler_, Jan 27 2013
%C A022521 Numbers that can be arranged in a triangular-antitegmatic icosachoron (the 4D version of "rhombic dodecahedal numbers" (A005917)). - _Steven Lu_, Mar 28 2023
%D A022521 John H. Conway and Richard K. Guy, The Book of Numbers, Copernicus Press, NY, 1996, p. 54.
%H A022521 Vincenzo Librandi, <a href="/A022521/b022521.txt">Table of n, a(n) for n = 0..10000</a>
%H A022521 Polytope Wiki, <a href="https://polytope.miraheze.org/wiki/Triangular-antitegmatic_icosachoron">Triangular-antitegmatic Icosachoron</a>
%H A022521 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F A022521 a(n) = A003215(n) + 24 * A006322(n). - Xavier Acloque, Oct 11 2003
%F A022521 G.f.: (-1-x^4-26*x^3-66*x^2-26*x)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
%F A022521 G.f.: polylog(-5, x)*(1-x)/x. See the g.f. of the rows of A008292 by _Vladeta Jovovic_, Sep 02 2002. - _Wolfdieter Lang_, May 10 2021
%F A022521 Sum_{n>=0} 1/a(n) = c1*tanh(c2/2) - c2*tanh(c1/2), where c1 = tan(3*Pi/10)*Pi and c2 = tan(Pi/10)*Pi. - _Amiram Eldar_, Jan 27 2022
%t A022521 Table[(n+1)^5-n^5, {n,0,30}] (* _Vincenzo Librandi_, Nov 23 2011 *)
%o A022521 (Magma) [(n+1)^5-n^5: n in [0..30]]; // _Vincenzo Librandi_, Nov 23 2011
%o A022521 (PARI) a(n)=(n+1)^5-n^5 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A022521 First differences of A000584.
%Y A022521 Column k=4 of array A047969.
%Y A022521 Cf. A003215, A005917, A006322, A008292, A019916, A019952, A022522.
%K A022521 nonn,easy
%O A022521 0,2
%A A022521 _N. J. A. Sloane_