OFFSET
1,1
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).
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).
From Amiram Eldar, Oct 27 2025: (Start)
Sum_{n>=1} 1/a(n) = (5/4)*log(5/4).
Sum_{n>=1} (-1)^(n+1)/a(n) = (5/4)*log(6/5). (End)
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 *)
PROG
(PARI) mtrans(n, b) = n*(b-1)*b^(n-1);
for (n=1, 100, write("b212699.txt", n, " ", mtrans(n, 5)))
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Stanislav Sykora, May 25 2012
STATUS
approved
