OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..3312
FORMULA
G.f.: Sum_{k>=2} x^Fibonacci(k)*(1-x)^2/(1-2*x)^2.
a(n) ~ c * 2^n * n, where c = 0.22756969930196647294851075611776578612085598114... - Vaclav Kotesovec, Aug 18 2019
c = A124091/4 - 3/8. - Vaclav Kotesovec, Mar 17 2024
MAPLE
a:= proc(n) option remember; add(a(n-j)+`if`((t->issqr(t+4)
or issqr(t-4))(5*j^2), ceil(2^(n-j-1)), 0), j=1..n)
end:
seq(a(n), n=0..33);
MATHEMATICA
a[n_] := a[n] = Sum[a[n - j] + With[{t = 5 j^2}, If[IntegerQ@Sqrt[t + 4] || IntegerQ@Sqrt[t - 4], Ceiling[2^(n - j - 1)], 0]], {j, 1, n}];
a /@ Range[0, 33] (* Jean-François Alcover, Dec 29 2020, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 06 2019
STATUS
approved