OFFSET
0,2
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (12,-36).
FORMULA
a(n) = 12*a(n-1) - 36*a(n-2).
G.f.: (1+6*x)/(1-6*x)^2.
a(n) = 6*a(n-1) + 2*6^n. - Vincenzo Librandi, Nov 05 2011
From Amiram Eldar, Dec 10 2022: (Start)
Sum_{n>=0} 1/a(n) = sqrt(6)*arccoth(sqrt(6)).
Sum_{n>=0} (-1)^n/a(n) = sqrt(6)*arccot(sqrt(6)). (End)
E.g.f.: exp(6*x)*(1 + 12*x). - Stefano Spezia, May 07 2023
MATHEMATICA
a[n_] := (2*n + 1)*6^n; Array[a, 25, 0] (* Amiram Eldar, Dec 10 2022 *)
PROG
(Magma) [(2*n+1)*6^n: n in [0..30]]; // Vincenzo Librandi, Nov 05 2011
(PARI) a(n) = (2*n+1)*6^n \\ Amiram Eldar, Dec 10 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Nov 04 2011
STATUS
approved