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%I #20 Nov 18 2019 22:06:17
%S 6,84,882,8232,72030,605052,4941258,39530064,311299254,2421216420,
%T 18643366434,142367525496,1079620401678,8138676874188,61040076556410,
%U 455765904954528,3389758918099302,25124095510618356,185639150161791186,1367867422244777160
%N Main transitions in systems of n particles with spin 3.
%C Please, refer to the general explanation in A212697.
%C This sequence is for base b=7 (see formula), corresponding to spin S=(b-1)/2=3.
%H Stanislav Sykora, <a href="/A212701/b212701.txt">Table of n, a(n) for n = 1..100</a>
%H 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 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49).
%F a(n) = n*(b-1)*b^(n-1). For this sequence, set b=7.
%F a(n) = 14*a(n-1)-49*a(n-2). - _Colin Barker_, Jun 16 2015
%F G.f.: 6*x / (7*x-1)^2. - _Colin Barker_, Jun 16 2015
%t LinearRecurrence[{14,-49},{6,84},20] (* _Harvey P. Dale_, Aug 02 2016 *)
%o (PARI): mtrans(n, b) = n*(b-1)*b^(n-1);
%o for (n=1, 100, write("b212701.txt", n, " ", mtrans(n, 7)))
%o (PARI) Vec(6*x/(7*x-1)^2 + O(x^100)) \\ _Colin Barker_, Jun 16 2015
%Y Cf. A001787, A212697, A212698, A212699, A212700, A212702, A212703, A212704 (b = 2, 3, 4, 5, 6, 8, 9, 10).
%K nonn,easy
%O 1,1
%A _Stanislav Sykora_, May 25 2012
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