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

6, 84, 882, 8232, 72030, 605052, 4941258, 39530064, 311299254, 2421216420, 18643366434, 142367525496, 1079620401678, 8138676874188, 61040076556410, 455765904954528, 3389758918099302, 25124095510618356, 185639150161791186, 1367867422244777160, 10053825553499112126

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=7 (see formula), corresponding to spin S=(b-1)/2=3.

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 (14,-49).

Crossrefs

Cf. A001787, A212697, A212698, A212699, A212700, A212702, A212703, A212704 (b = 2, 3, 4, 5, 6, 8, 9, 10).

Cf. A000420, A008588, A027473.

Programs

Mathematica

LinearRecurrence[{14,-49},{6,84},20] (* Harvey P. Dale, Aug 02 2016 *)

PARI

mtrans(n, b) = n*(b-1)*b^(n-1);
for (n=1, 100, write("b212701.txt", n, " ", mtrans(n, 7)))

PARI

Vec(6*x/(7*x-1)^2 + O(x^100)) \\ Colin Barker, Jun 16 2015

Formula

a(n) = n*(b-1)*b^(n-1). For this sequence, set b=7.

From Colin Barker, Jun 16 2015: (Start)

a(n) = 14*a(n-1) - 49*a(n-2) for n > 2.

G.f.: 6*x/(7*x-1)^2. (End)

From Elmo R. Oliveira, May 14 2025: (Start)

E.g.f.: 6*x*exp(7*x).

a(n) = 6*A027473(n) = A008588(n)*A000420(n-1). (End)