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 A212699 #28 May 14 2025 09:09:14
%S A212699 4,40,300,2000,12500,75000,437500,2500000,14062500,78125000,429687500,
%T A212699 2343750000,12695312500,68359375000,366210937500,1953125000000,
%U A212699 10375976562500,54931640625000,289916992187500,1525878906250000,8010864257812500,41961669921875000,219345092773437500
%N A212699 Main transitions in systems of n particles with spin 2.
%C A212699 Please, refer to the general explanation in A212697.
%C A212699 This particular sequence is obtained for base b=5, corresponding to spin S=(b-1)/2=2.
%H A212699 Stanislav Sykora, <a href="/A212699/b212699.txt">Table of n, a(n) for n = 1..100</a>
%H A212699 Stanislav Sýkora, <a href="http://www.ebyte.it/stan/blog12to14.html#14Dec31">Magnetic Resonance on OEIS</a>, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
%H A212699 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-25).
%F A212699 a(n) = n*(b-1)*b^(n-1) where b=5.
%F A212699 a(n) = 10*a(n-1) - 25*a(n-2), a(0)=a(1)=4, a(2)=40. - _Harvey P. Dale_, Aug 19 2014
%F A212699 From _Elmo R. Oliveira_, May 13 2025: (Start)
%F A212699 G.f.: 4*x/(5*x-1)^2.
%F A212699 E.g.f.: 4*x*exp(5*x).
%F A212699 a(n) = 4*A053464(n) = A008586(n)*A000351(n-1). (End)
%t A212699 Join[{4},Table[4n*5^(n-1),{n,20}]] (* or *) Join[{4},LinearRecurrence[{10,-25},{4,40},20]] (* _Harvey P. Dale_, Aug 19 2014 *)
%o A212699 (PARI) mtrans(n, b) = n*(b-1)*b^(n-1);
%o A212699 for (n=1, 100, write("b212699.txt", n, " ", mtrans(n, 5)))
%Y A212699 Cf. A001787, A212697, A212698, A212700, A212701, A212702, A212703, A212704 (b = 2, 3, 4, 6, 7, 8, 9, 10).
%Y A212699 Cf. A000351, A008586, A053464.
%K A212699 nonn,easy
%O A212699 1,1
%A A212699 _Stanislav Sykora_, May 25 2012