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 A008414 #37 Nov 17 2023 12:10:17
%S A008414 1,12,72,292,912,2364,5336,10836,20256,35436,58728,93060,142000,
%T A008414 209820,301560,423092,581184,783564,1038984,1357284,1749456,2227708,
%U A008414 2805528,3497748,4320608,5291820,6430632,7757892,9296112,11069532
%N A008414 Coordination sequence for 6-dimensional cubic lattice.
%C A008414 If Y_i (i=1,2,3,4,5,6) are 2-blocks of a (n+6)-set X then a(n-5) is the number of 11-subsets of X intersecting each Y_i (i=1,2,3,4,5,6). - _Milan Janjic_, Oct 28 2007
%H A008414 Seiichi Manyama, <a href="/A008414/b008414.txt">Table of n, a(n) for n = 0..10000</a>
%H A008414 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H A008414 Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Two Enumerative Functions</a>
%H A008414 Milan Janjić, <a href="https://arxiv.org/abs/1905.04465">On Restricted Ternary Words and Insets</a>, arXiv:1905.04465 [math.CO], 2019.
%H A008414 Ross McPhedran, <a href="https://arxiv.org/abs/2311.06294">Numerical Investigations of the Keiper-Li Criterion for the Riemann Hypothesis</a>, arXiv:2311.06294 [math.NT], 2023. See p. 6.
%H A008414 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6, -15, 20, -15, 6, -1).
%F A008414 G.f.: ((1+x)/(1-x))^6.
%F A008414 a(n) = 4*n*(2/15*n^4+4/3*n^2+23/15) for n > 0. - S. Bujnowski (slawb(AT)atr.bydgoszcz.pl), Nov 26 2002
%F A008414 n*a(n) = 12*a(n-1) + (n-2)*a(n-2) for n > 1. - _Seiichi Manyama_, Jun 06 2018
%p A008414 for n from 1 to 8 do eval(4*n*(2/15*n^4+4/3*n^2+23/15)) od;
%t A008414 {1}~Join~Table[4 n (2/15 n^4 + 4/3 n^2 + 23/15), {n, 29}] (* or *)
%t A008414 CoefficientList[Series[((1 + x)/(1 - x))^6, {x, 0, 29}], x] (* _Michael De Vlieger_, Oct 04 2016 *)
%t A008414 LinearRecurrence[{6,-15,20,-15,6,-1},{1,12,72,292,912,2364,5336},30] (* _Harvey P. Dale_, Jul 01 2020 *)
%o A008414 (PARI) a(n)=if(n, 4*n*(2*n^4+20*n^2+23)/15, 1) \\ _Charles R Greathouse IV_, Oct 04 2016
%K A008414 nonn,easy
%O A008414 0,2
%A A008414 _N. J. A. Sloane_