A212699 Main transitions in systems of n particles with spin 2.

4, 40, 300, 2000, 12500, 75000, 437500, 2500000, 14062500, 78125000, 429687500, 2343750000, 12695312500, 68359375000, 366210937500, 1953125000000, 10375976562500, 54931640625000, 289916992187500, 1525878906250000, 8010864257812500, 41961669921875000, 219345092773437500

Offset: 1

Author

Stanislav Sykora, May 25 2012

Keywords

• nonn
• easy

Comments

Please, refer to the general explanation in A212697.

This particular sequence is obtained for base b=5, corresponding to spin S=(b-1)/2=2.

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 (10,-25).

Crossrefs

Cf. A001787, A212697, A212698, A212700, A212701, A212702, A212703, A212704 (b = 2, 3, 4, 6, 7, 8, 9, 10).

Cf. A000351, A008586, A053464.

Programs

Mathematica

Join[{4},Table[4n*5^(n-1),{n,20}]] (* or *) Join[{4},LinearRecurrence[{10,-25},{4,40},20]] (* Harvey P. Dale, Aug 19 2014 *)

PARI

mtrans(n, b) = n*(b-1)*b^(n-1);
for (n=1, 100, write("b212699.txt", n, " ", mtrans(n, 5)))

Formula

a(n) = n*(b-1)*b^(n-1) where b=5.

a(n) = 10*a(n-1) - 25*a(n-2), a(0)=a(1)=4, a(2)=40. - Harvey P. Dale, Aug 19 2014

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

G.f.: 4*x/(5*x-1)^2.

E.g.f.: 4*x*exp(5*x).

a(n) = 4*A053464(n) = A008586(n)*A000351(n-1). (End)