OFFSET
0,7
COMMENTS
LINKS
Indranil Ghosh, Table of n, a(n) for n = 0..1000
FORMULA
G.f.: x / (1 - x - x^2) - Sum_{k>=1} k! * x^(k*(k + 1)/2) / Product_{j=1..k} (1 - x^j). - Ilya Gutkovskiy, Jan 30 2020
MATHEMATICA
T[n_, k_] := T[n, k] = If[k<0 || n<0, 0, If[k==0, If[n==0, 1, 0], T[n - k, k] + k*T[n - k, k - 1]]]; a[n_] := Sum[T[n, k], {k, 0, Floor[(Sqrt[8*n + 1] - 1) / 2]}]; Table[If[n==0, 0, Fibonacci[n] - a[n]], {n, 0, 43}](* Indranil Ghosh, Mar 09 2017, after Jean-François Alcover and Alois P. Heinz *)
PROG
(PARI) T(n, k) = if(k<0 || n<0, 0, if(k==0, if(n==0, 1, 0), T(n - k, k) + k*T(n - k, k - 1)));
a(n) = sum(k=0, floor(sqrt(8*n + 1) - 1), T(n, k));
for (n=0, 43, print1(if(n==0, 0, fibonacci(n) - a(n)), ", ")) \\ Indranil Ghosh, Mar 09 2017
CROSSREFS
KEYWORD
sign
AUTHOR
N. J. A. Sloane, Feb 24 2017
STATUS
approved