OFFSET
0,1
COMMENTS
Trisection of A055998.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Leo Tavares, Illustration: Triangulated Triangles.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
G.f.: (-7-4*x+2*x^2)/(x-1)^3.
a(n) = a(n-1) + 9*(n+1) = (14 + 27*n + 9*n^2)/2.
a(n) = 2*a(n-1) - a(n-2) + 9.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
a(n) mod 9 = A153466(n) mod 9 = 7.
Sum_{n>=0} 1/a(n) = 1/2-2*Pi*sqrt(3)/45 = 0.2581600... - R. J. Mathar, Apr 07 2011
Sum_{n>=0} (-1)^n/a(n) = 3/10 - 4*log(2)/15. - Amiram Eldar, Mar 27 2022
From Elmo R. Oliveira, Oct 30 2024: (Start)
E.g.f.: exp(x)*(7 + 18*x + 9*x^2/2).
MAPLE
MATHEMATICA
a[n_] := (3*n + 7)*(3*n + 2)/2; Array[a, 50, 0] (* Amiram Eldar, Mar 27 2022 *)
PROG
(Magma) [(3*n+7)*(3*n+2)/2: n in [0..50]]; // Vincenzo Librandi, Aug 04 2011
(PARI) a(n)=(3*n+7)*(3*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
Paul Curtz, Jan 12 2011
STATUS
approved