OFFSET
0,1
COMMENTS
Old name was: "Numbers of the form x^2 + 22".
x^2 + 22 != y^n for all x,y and n > 1.
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).
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(22 - 43*x + 23*x^2)/(1 - x)^3. - Vincenzo Librandi, Apr 30 2014
From Amiram Eldar, Nov 04 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(22)*Pi*coth(sqrt(22)*Pi))/44.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(22)*Pi*cosech(sqrt(22)*Pi))/44. (End)
MATHEMATICA
Table[n^2 + 22, {n, 0, 60}] (* Vincenzo Librandi, Apr 30 2014 *)
PROG
(PARI) a(n)=n^2+22 \\ Amiram Eldar, Nov 04 2020
(Magma) [n^2+22: n in [0..60]]; // Vincenzo Librandi, Apr 30 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Cino Hilliard, Feb 21 2006
EXTENSIONS
a(0)=22 from Vincenzo Librandi, Apr 30 2014
Definition changed by Bruno Berselli, Mar 13 2015
Offset corrected by Amiram Eldar, Nov 04 2020
STATUS
approved