|
|
A191797
|
|
a(n) = binomial(F(n), 2) where F(n) = A000045(n).
|
|
6
|
|
|
0, 0, 0, 1, 3, 10, 28, 78, 210, 561, 1485, 3916, 10296, 27028, 70876, 185745, 486591, 1274406, 3337236, 8738290, 22879230, 59901985, 156830905, 410597496, 1074972528, 2814337800, 7368069528, 19289917153, 50501756955, 132215475106, 346144864780, 906219437046
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
FORMULA
|
a(n) = +3*a(n-1) + 1*a(n-2) - 5*a(n-3) - 1*a(n-4) + 1*a(n-5).
G.f.: x^3/(1-3*x-x^2+5*x^3+x^4-x^5) = x^3/((1+x)*(1-x-x^2)*(1-3*x+x^2)).
a(n) = (2^(-1-n)*(-(-1)^n*2^(1+n) + sqrt(5)*(1-sqrt(5))^n + (3-sqrt(5))^n - sqrt(5)*(1+sqrt(5))^n + (3+sqrt(5))^n)) / 5. - Colin Barker, Mar 26 2017
|
|
EXAMPLE
|
a(7) = binomial(13,2) = 78.
|
|
MAPLE
|
with(combinat): seq(binomial(fibonacci(n), 2), n = 0 .. 30);
|
|
MATHEMATICA
|
Table[Binomial[Fibonacci[n], 2], {n, 0, 39}] (* Alonso del Arte, Apr 04 2013 *)
|
|
PROG
|
(PARI) a(n) = binomial(fibonacci(n), 2); \\ Michel Marcus, Sep 07 2015
(PARI) concat(vector(3), Vec(x^3 / ((1+x)*(1-x-x^2)*(1-3*x+x^2)) + O(x^40))) \\ Colin Barker, Mar 26 2017
(Python)
from sympy import binomial, fibonacci
def a(n): return binomial(fibonacci(n), 2) # Indranil Ghosh, Mar 26 2017
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|