cp's OEIS Frontend

A212702 Main transitions in systems of n particles with spin 7/2.

%I A212702 #25 May 15 2025 01:02:18
%S A212702 7,112,1344,14336,143360,1376256,12845056,117440512,1056964608,
%T A212702 9395240960,82678120448,721554505728,6253472382976,53876069761024,
%U A212702 461794883665920,3940649673949184,33495522228568064,283726776524341248,2395915001761103872,20176126330619822080
%N A212702 Main transitions in systems of n particles with spin 7/2.
%C A212702 Please, refer to the general explanation in A212697.
%C A212702 This sequence is for base b=8 (see formula), corresponding to spin S=(b-1)/2=7/2.
%H A212702 Stanislav Sykora, <a href="/A212702/b212702.txt">Table of n, a(n) for n = 1..100</a>
%H A212702 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 A212702 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16,-64).
%F A212702 a(n) = n*(b-1)*b^(n-1). For this sequence, set b=8.
%F A212702 From _Colin Barker_, Jun 16 2015: (Start)
%F A212702 a(n) = 16*a(n-1) - 64*a(n-2) for n > 2.
%F A212702 G.f.: 7*x/(8*x-1)^2. (End)
%F A212702 From _Elmo R. Oliveira_, May 14 2025: (Start)
%F A212702 E.g.f.: 7*x*exp(8*x).
%F A212702 a(n) = 7*A053539(n) = A008589(n)*A001018(n-1). (End)
%t A212702 LinearRecurrence[{16,-64},{7,112},30] (* _Harvey P. Dale_, Feb 11 2016 *)
%o A212702 (PARI) mtrans(n, b) = n*(b-1)*b^(n-1);
%o A212702 for (n=1, 100, write("b212702.txt", n, " ", mtrans(n, 8)))
%o A212702 (PARI) Vec(7*x/(8*x-1)^2 + O(x^100)) \\ _Colin Barker_, Jun 16 2015
%Y A212702 Cf. A001787, A212697, A212698, A212699, A212700, A212701, A212703, A212704 (b = 2, 3, 4, 5, 6, 7, 9, 10).
%Y A212702 Cf. A001018, A008589, A053539.
%K A212702 nonn,easy
%O A212702 1,1
%A A212702 _Stanislav Sykora_, May 25 2012