cp's OEIS Frontend

A212701 Main transitions in systems of n particles with spin 3.

%I A212701 #26 May 15 2025 01:02:47
%S A212701 6,84,882,8232,72030,605052,4941258,39530064,311299254,2421216420,
%T A212701 18643366434,142367525496,1079620401678,8138676874188,61040076556410,
%U A212701 455765904954528,3389758918099302,25124095510618356,185639150161791186,1367867422244777160,10053825553499112126
%N A212701 Main transitions in systems of n particles with spin 3.
%C A212701 Please, refer to the general explanation in A212697.
%C A212701 This sequence is for base b=7 (see formula), corresponding to spin S=(b-1)/2=3.
%H A212701 Stanislav Sykora, <a href="/A212701/b212701.txt">Table of n, a(n) for n = 1..100</a>
%H A212701 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 A212701 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-49).
%F A212701 a(n) = n*(b-1)*b^(n-1). For this sequence, set b=7.
%F A212701 From _Colin Barker_, Jun 16 2015: (Start)
%F A212701 a(n) = 14*a(n-1) - 49*a(n-2) for n > 2.
%F A212701 G.f.: 6*x/(7*x-1)^2. (End)
%F A212701 From _Elmo R. Oliveira_, May 14 2025: (Start)
%F A212701 E.g.f.: 6*x*exp(7*x).
%F A212701 a(n) = 6*A027473(n) = A008588(n)*A000420(n-1). (End)
%t A212701 LinearRecurrence[{14,-49},{6,84},20] (* _Harvey P. Dale_, Aug 02 2016 *)
%o A212701 (PARI) mtrans(n, b) = n*(b-1)*b^(n-1);
%o A212701 for (n=1, 100, write("b212701.txt", n, " ", mtrans(n, 7)))
%o A212701 (PARI) Vec(6*x/(7*x-1)^2 + O(x^100)) \\ _Colin Barker_, Jun 16 2015
%Y A212701 Cf. A001787, A212697, A212698, A212699, A212700, A212702, A212703, A212704 (b = 2, 3, 4, 5, 6, 8, 9, 10).
%Y A212701 Cf. A000420, A008588, A027473.
%K A212701 nonn,easy
%O A212701 1,1
%A A212701 _Stanislav Sykora_, May 25 2012