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

8, 144, 1944, 23328, 262440, 2834352, 29760696, 306110016, 3099363912, 30993639120, 306837027288, 3012581722464, 29372671794024, 284688972772848, 2745215094595320, 26354064908115072, 252010745683850376, 2401514164751985936, 22814384565143866392, 216136274827678734240

Offset: 1

Author

Stanislav Sykora, May 25 2012

Keywords

• nonn
• easy

Comments

Please, refer to the general explanation in A212697.

This sequence is for base b=9 (see formula), corresponding to spin S=(b-1)/2=4.

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..100
• Stanislav Sýkora, Magnetic Resonance on OEIS, Stan's NMR Blog (Dec 31, 2014), Retrieved Nov 12, 2019.
• Index entries for linear recurrences with constant coefficients, signature (18,-81).

Crossrefs

Cf. A001787, A212697, A212698, A212699, A212700, A212701, A212702, A212704 (b = 2, 3, 4, 5, 6, 7, 8, 10).

Cf. A001019, A008590, A053540.

Programs

Mathematica

LinearRecurrence[{18,-81},{8,144},30] (* Harvey P. Dale, Jun 28 2017 *)

PARI

mtrans(n, b) = n*(b-1)*b^(n-1);
for (n=1, 100, write("b212703.txt", n, " ", mtrans(n, 9)))

PARI

Vec(8*x/(9*x-1)^2 + O(x^100)) \\ Colin Barker, Jun 16 2015

PARI

a(n)=8*n*9^(n-1) \\ Charles R Greathouse IV, Jun 16 2015

Formula

a(n) = n*(b-1)*b^(n-1). For this sequence, set b=9.

From Colin Barker, Jun 16 2015: (Start)

a(n) = 18*a(n-1) - 81*a(n-2) for n > 2.

G.f.: 8*x/(9*x-1)^2. (End)

From Elmo R. Oliveira, May 13 2025: (Start)

E.g.f.: 8*x*exp(9*x).

a(n) = 8*A053540(n) = A008590(n)*A001019(n-1). (End)