OFFSET
1,2
COMMENTS
LINKS
FORMULA
G.f.: Sum_{k>=2} x^Fibonacci(k)/(1 - x^Fibonacci(k)) / Product_{k>=2} (1 - x^Fibonacci(k)).
a(n) = Sum_{k=1..n} k * A319394(n,k). - Alois P. Heinz, Sep 18 2018
EXAMPLE
a(5) = 18 because we have [5], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and 1 + 2 + 3 + 3 + 4 + 5 = 18.
MAPLE
h:= proc(n) option remember; `if`(n<1, 0, `if`((t->
issqr(t+4) or issqr(t-4))(5*n^2), n, h(n-1)))
end:
b:= proc(n, i) option remember; `if`(n=0 or i=1, [1, n],
b(n, h(i-1))+(p->p+[0, p[1]])(b(n-i, h(min(n-i, i)))))
end:
a:= n-> b(n, h(n))[2]:
seq(a(n), n=1..70); # Alois P. Heinz, Sep 18 2018
MATHEMATICA
Rest[CoefficientList[Series[Sum[x^Fibonacci[k]/(1 - x^Fibonacci[k]), {k, 2, 20}]/Product[1 - x^Fibonacci[k], {k, 2, 20}], {x, 0, 52}], x]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 27 2017
STATUS
approved