OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
From Vincenzo Librandi, Jul 10 2012: (Start)
G.f.: 2*(1+12*x+3*x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). (End)
From Amiram Eldar, Mar 01 2022: (Start)
Sum_{n>=0} 1/a(n) = Pi/8 + log(2)/4.
Sum_{n>=0} (-1)^n/a(n) = ((sqrt(2)-1)*Pi + sqrt(2)*log((2+sqrt(2))/(2-sqrt(2))))/8. (End)
From Elmo R. Oliveira, Oct 30 2024: (Start)
E.g.f.: 2*exp(x)*(1 + 14*x + 8*x^2).
MATHEMATICA
Table[(4n+1)*(4n+2), {n, 0, 50}] (* Vincenzo Librandi, Jul 10 2012 *)
PROG
(Magma) (4*n+1)*(4*n+2); // Vincenzo Librandi Jul 10 2012
(PARI) a(n)=(4*n+1)*(4*n+2) \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
SUNKU Sai Swaroop (sai2020(AT)gmail.com), Mar 08 2009
EXTENSIONS
Definition corrected and sequence extended by R. J. Mathar, Mar 11 2009
STATUS
approved