OFFSET
0,1
COMMENTS
The only solution for x at the Diophantine equation x^2 + 20 = y^m (with m>2) is 14: 14^2 + 20 = a(14) = 6^3. - Bruno Berselli, May 01 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
J. H. E. Cohn, The diophantine equation x^2 + C = y^n, Acta Arithmetica LXV.4, 1993, p. 379.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (20 - 39*x + 21*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.
From Amiram Eldar, Nov 03 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(20)*Pi*coth(sqrt(20)*Pi))/40.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(20)*Pi*cosech(sqrt(20)*Pi))/40. (End)
MATHEMATICA
Table[n^2 + 20, {n, 0, 60}]
PROG
(Magma) [n^2+20: n in [0..60]];
(PARI) a(n)=n^2+20 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, May 01 2014
STATUS
approved