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

7, 112, 1344, 14336, 143360, 1376256, 12845056, 117440512, 1056964608, 9395240960, 82678120448, 721554505728, 6253472382976, 53876069761024, 461794883665920, 3940649673949184, 33495522228568064, 283726776524341248, 2395915001761103872, 20176126330619822080

Offset

1,1

Comments

Please, refer to the general explanation in A212697.

This sequence is for base b=8 (see formula), corresponding to spin S=(b-1)/2=7/2.

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 (16,-64).

Formula

a(n) = n*(b-1)*b^(n-1). For this sequence, set b=8.

From Colin Barker, Jun 16 2015: (Start)

a(n) = 16*a(n-1) - 64*a(n-2) for n > 2.

G.f.: 7*x/(8*x-1)^2. (End)

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

E.g.f.: 7*x*exp(8*x).

a(n) = 7*A053539(n) = A008589(n)*A001018(n-1). (End)

From Amiram Eldar, Oct 27 2025: (Start)

Sum_{n>=1} 1/a(n) = (8/7)*log(8/7).

Sum_{n>=1} (-1)^(n+1)/a(n) = (8/7)*log(9/8). (End)

Mathematica

LinearRecurrence[{16, -64}, {7, 112}, 30] (* Harvey P. Dale, Feb 11 2016 *)

Prog

(PARI) mtrans(n, b) = n*(b-1)*b^(n-1);
for (n=1, 100, write("b212702.txt", n, " ", mtrans(n, 8)))
(PARI) Vec(7*x/(8*x-1)^2 + O(x^100)) \\ Colin Barker, Jun 16 2015

Crossrefs

Cf. A001787, A212697, A212698, A212699, A212700, A212701, A212703, A212704 (b = 2, 3, 4, 5, 6, 7, 9, 10).

Cf. A001018, A008589, A053539.

Sequence in context: A117795 A163700 A094219 * A217223 A067404 A129030

Adjacent sequences: A212699 A212700 A212701 * A212703 A212704 A212705

Keyword

nonn,easy

Author

Stanislav Sykora, May 25 2012

Status

approved