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 A004466 #46 Sep 08 2022 08:44:33
%S A004466 0,1,12,43,104,205,356,567,848,1209,1660,2211,2872,3653,4564,5615,
%T A004466 6816,8177,9708,11419,13320,15421,17732,20263,23024,26025,29276,32787,
%U A004466 36568,40629,44980,49631,54592
%N A004466 a(n) = n*(5*n^2 - 2)/3.
%C A004466 3-dimensional analog of centered polygonal numbers.
%C A004466 Also as a(n)=(1/6)*(10*n^3-4*n), n>0: structured pentagonal anti-diamond numbers (vertex structure 11) (Cf. A051673 = alternate vertex A100188 = structured anti-diamonds; A100145 for more on structured numbers). - James A. Record (james.record(AT)gmail.com), Nov 07 2004
%C A004466 a(n+1)-10*a(n) = (n+1)*(5*(n+1)^2-2)/3 - (10n(n+1)(n+2)/6) = n. The unit digits are 0,1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,... . - _Eric Desbiaux_, Aug 18 2008
%D A004466 E. Deza and M. M. Deza, Figurate numbers, World Scientific Publishing (2012), page 140.
%H A004466 Vincenzo Librandi, <a href="/A004466/b004466.txt">Table of n, a(n) for n = 0..5000</a>
%H A004466 T. P. Martin, <a href="http://dx.doi.org/10.1016/0370-1573(95)00083-6">Shells of atoms</a>, Phys. Reports, 273 (1996), 199-241, eq. (11).
%H A004466 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-6,4,-1).
%F A004466 G.f.: x*(1+8*x+x^2)/(1-x)^4. - _Colin Barker_, Jan 08 2012
%F A004466 E.g.f.: (x/3)*(3 + 15*x + 5*x^2)*exp(x). - _G. C. Greubel_, Sep 01 2017
%p A004466 A004466:=n->n*(5*n^2 - 2)/3; seq(A004466(n), n=0..50); # _Wesley Ivan Hurt_, Mar 10 2014
%t A004466 Table[n(5n^2-2)/3,{n,0,80}] (* _Vladimir Joseph Stephan Orlovsky_, Apr 18 2011 *)
%o A004466 (Magma) [n*(5*n^2-2)/3: n in [0..50]]; // _Vincenzo Librandi_, May 15 2011
%o A004466 (PARI) a(n)=n*(5*n^2-2)/3 \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A004466 Cf. A062786 (first differences), A264853 (partial sums).
%Y A004466 1/12*t*(n^3-n)+n for t = 2, 4, 6, ... gives A004006, A006527, A006003, A005900, A004068, A000578, A004126, A000447, A004188, A004466, A004467, A007588, A062025, A063521, A063522, A063523.
%K A004466 nonn,easy
%O A004466 0,3
%A A004466 Albert D. Rich (Albert_Rich(AT)msn.com)