OFFSET
0,3
COMMENTS
Consider the Lyman spectrum of Hydrogen A005563(n)/A000290(n+1) = n*(n+2)/(n+1)^2 = 0/1, 3/4, 8/9, 15/16, ...
The first differences of these fractions are 3/4, 5/36, 7/144, 9/400, 11/900, 13/1764, 15/3136, ... = (2n+1)/(n*(n+1))^2.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
FORMULA
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 24.
G.f.: (-1 + 6*x + 16*x^2 + 2*x^3 + x^4)/(1-x)^5.
PROG
(Magma) [-1 -2*n +n^2 +2*n^3 +n^4: n in [0..40]]; // Vincenzo Librandi, May 21 2011
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Paul Curtz, Sep 22 2009
EXTENSIONS
Edited and extended by R. J. Mathar, Feb 02 2010
STATUS
approved