OFFSET
1,2
COMMENTS
a(n) - 7*(n-1) is a triangular number. Sequence gives positive x values solving the Diophantine equation y^2 - 8*x = 113. - Bruno Berselli, Aug 27 2014
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: x*(1+4*x-4*x^2)/(1-x)^3.
a(n) = 3*a(n-1)-3*a(n-2)+a(n-3) = 2*a(n-1)-a(n-2)+1.
a(n+1) - a(n) = n + 5. - Jacques ALARDET, Aug 04 2015
Sum_{n>=1} 1/a(n) = 4919/8008 + 2*Pi*tan(sqrt(113)*Pi/2)/sqrt(113). - Amiram Eldar, Feb 25 2023
MATHEMATICA
Table[(n^2 + 9 n - 8)/2, {n, 1, 60}]
PROG
(Magma) [(n^2+9*n-8)/2: n in [1..60]];
(Sage) [(n^2+9*n-8)/2 for n in (1..60)] # Bruno Berselli, Aug 27 2014
(PARI) a(n)=(n^2+9*n-8)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Aug 24 2014
STATUS
approved