cp's OEIS Frontend

A212703 Main transitions in systems of n particles with spin 4.

%I A212703 #24 May 14 2025 09:09:18
%S A212703 8,144,1944,23328,262440,2834352,29760696,306110016,3099363912,
%T A212703 30993639120,306837027288,3012581722464,29372671794024,
%U A212703 284688972772848,2745215094595320,26354064908115072,252010745683850376,2401514164751985936,22814384565143866392,216136274827678734240
%N A212703 Main transitions in systems of n particles with spin 4.
%C A212703 Please, refer to the general explanation in A212697.
%C A212703 This sequence is for base b=9 (see formula), corresponding to spin S=(b-1)/2=4.
%H A212703 Stanislav Sykora, <a href="/A212703/b212703.txt">Table of n, a(n) for n = 1..100</a>
%H A212703 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 A212703 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-81).
%F A212703 a(n) = n*(b-1)*b^(n-1). For this sequence, set b=9.
%F A212703 From _Colin Barker_, Jun 16 2015: (Start)
%F A212703 a(n) = 18*a(n-1) - 81*a(n-2) for n > 2.
%F A212703 G.f.: 8*x/(9*x-1)^2. (End)
%F A212703 From _Elmo R. Oliveira_, May 13 2025: (Start)
%F A212703 E.g.f.: 8*x*exp(9*x).
%F A212703 a(n) = 8*A053540(n) = A008590(n)*A001019(n-1). (End)
%t A212703 LinearRecurrence[{18,-81},{8,144},30] (* _Harvey P. Dale_, Jun 28 2017 *)
%o A212703 (PARI) mtrans(n, b) = n*(b-1)*b^(n-1);
%o A212703 for (n=1, 100, write("b212703.txt", n, " ", mtrans(n, 9)))
%o A212703 (PARI) Vec(8*x/(9*x-1)^2 + O(x^100)) \\ _Colin Barker_, Jun 16 2015
%o A212703 (PARI) a(n)=8*n*9^(n-1) \\ _Charles R Greathouse IV_, Jun 16 2015
%Y A212703 Cf. A001787, A212697, A212698, A212699, A212700, A212701, A212702, A212704 (b = 2, 3, 4, 5, 6, 7, 8, 10).
%Y A212703 Cf. A001019, A008590, A053540.
%K A212703 nonn,easy
%O A212703 1,1
%A A212703 _Stanislav Sykora_, May 25 2012