OFFSET
0,1
LINKS
Ivan Panchenko, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (-8*x^2 + 13*x - 7)/(x - 1)^3. - Indranil Ghosh, Apr 05 2017
From Amiram Eldar, Nov 02 2020: (Start)
Sum_{n>=0} 1/a(n) = (1 + sqrt(7)*Pi*coth(sqrt(7)*Pi))/14.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(7)*Pi*cosech(sqrt(7)*Pi))/14. (End)
From Amiram Eldar, Feb 05 2024: (Start)
Product_{n>=0} (1 - 1/a(n)) = sqrt(6/7)*sinh(sqrt(6)*Pi)/sinh(sqrt(7)*Pi).
Product_{n>=0} (1 + 1/a(n)) = 2*sqrt(2/7)*sinh(2*sqrt(2)*Pi)/sinh(sqrt(7)*Pi). (End)
MATHEMATICA
Table[n^2 + 7, {n, 0, 60}] (* Stefan Steinerberger, Apr 08 2006 *)
PROG
(PARI) a(n) = n^2 + 7 \\ Indranil Ghosh, Apr 05 2017
(Python) def a(n): return n**2 + 7 # Indranil Ghosh, Apr 05 2017
CROSSREFS
KEYWORD
nonn,less,easy
AUTHOR
Parthasarathy Nambi, Apr 07 2006
EXTENSIONS
More terms from Stefan Steinerberger, Apr 08 2006
STATUS
approved