OFFSET
0,3
COMMENTS
LINKS
Robert Israel, Table of n, a(n) for n = 0..1195
A. Radhakrishnan, L. Solus, and C. Uhler. Counting Markov equivalence classes for DAG models on trees, arXiv:1706.06091 [math.CO], 2017; Discrete Applied Mathematics 244 (2018): 170-185.
Index entries for linear recurrences with constant coefficients, signature (5,15,-15,-5,1).
FORMULA
G.f.: (-1 + 4*x + 8*x^2 + 11*x^3 - 4*x^4)/(-1 + 5*x + 15*x^2 - 15*x^3 - 5*x^4 + x^5). - Robert Israel, Aug 26 2018
MAPLE
f:= gfun:-rectoproc({a(n+5)-5*a(n+4)-15*a(n+3)+15*a(n+2)+5*a(n+1)-a(n), a(0)=1, a(1)=1, a(2)=12, a(3)=49, a(4)=409}, a(n), remember):
map(f, [$0..30]); # Robert Israel, Aug 26 2018
MATHEMATICA
Table[Fibonacci[n + 1]^4 - 4 Fibonacci[n - 1] Fibonacci[n]^3, {n, 0, 25}] (* Vincenzo Librandi, Aug 26 2018 *)
CoefficientList[Series[(-1 + 4 x + 8 x^2 + 11 x^3 - 4 x^4)/(-1 + 5 x + 15 x^2 - 15 x^3 - 5 x^4 + x^5), {x, 0, 50}], x] (* Stefano Spezia, Sep 03 2018 *)
PROG
(SageMath)
def a(n):
return fibonacci(n+1)^4-4*fibonacci(n-1)*fibonacci(n)^3
[a(n) for n in range(20)]
(Magma) [Fibonacci(n+1)^4-4*Fibonacci(n-1)*Fibonacci(n)^3: n in [0..25]]; // Vincenzo Librandi, Aug 26 2018
(PARI) a(n) = fibonacci(n+1)^4 - 4*fibonacci(n-1)*fibonacci(n)^3; \\ Michel Marcus, Aug 26 2018
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Liam Solus, Aug 26 2018
EXTENSIONS
a(0) = 1 prepended by Vincenzo Librandi, Aug 26 2018
STATUS
approved