OFFSET
0,2
LINKS
FORMULA
a(n) = C(n,0) + 11*C(n,1) + 9*C(n,2); binomial transform of (1, 11, 9, 0, 0, 0, ...).
a(n) = (9*n^2 + 13*n + 2)/2.
G.f.: (1 + 9*x - x^2)/(1-x)^3.
a(n) = 9*n + a(n-1) + 2 (with a(0)=1). - Vincenzo Librandi, Aug 08 2010
From Elmo R. Oliveira, Nov 16 2024: (Start)
E.g.f.: exp(x)*(9*x^2 + 22*x + 2)/2.
a(n) = A064226(n) - 2.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
EXAMPLE
a(1) = 9*1 + 1 + 2 = 12.
a(2) = 9*2 + 12 + 2 = 32.
a(3) = 9*3 + 32 + 2 = 61.
PROG
(PARI) a(n)=(9*n^2+13*n+2)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn,changed
AUTHOR
Paul Barry, Mar 15 2003
STATUS
approved