OFFSET
0,1
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Hacène Belbachir, Toufik Djellal, Jean-Gabriel Luque, On the self-convolution of generalized Fibonacci numbers, arXiv:1703.00323 [math.CO], 2017.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = A064226(n) + 2*n.
a(n) = 3*binomial(n,0) + 13*binomial(n,1) + 9*binomial(n,2); binomial transform of (3, 13, 9, 0, 0, 0, ...).
a(n) = (9*n^2 + 17*n + 6)/2.
G.f.: (3 + 7*x - x^2)/(1-x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Jul 08 2012
E.g.f.: exp(x)*(6 + 26*x + 9*x^2)/2. - Elmo R. Oliveira, Nov 13 2024
MATHEMATICA
CoefficientList[Series[(3+7x-x^2)/(1-x)^3, {x, 0, 50}], x] (* Vincenzo Librandi, Jul 08 2012 *)
PROG
(Magma) [(9*n^2+17*n+6)/2: n in [0..50]]; // Vincenzo Librandi, Jul 08 2012
(PARI) a(n)=(9*n^2+17*n+6)/2 \\ Charles R Greathouse IV, Jun 17 2017
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 15 2003
STATUS
approved