OFFSET
2,1
LINKS
G. C. Greubel, Table of n, a(n) for n = 2..5000
FORMULA
a(n) = Sum_{k=1..8} floor(p(n, k)/p(n-1, k)), where p(n, k) = n!/( Product_{i=1..floor(n/2^k)} A004001(i) ).
MATHEMATICA
Conway[n_]:= Conway[n]= If[n<3, 1, Conway[Conway[n-1]] +Conway[n-Conway[n-1]]];
f[n_, k_]:= f[n, k]= Product[Conway[i], {i, Floor[n/2^k]}];
a[n_]:= a[n]= Sum[Floor[n*f[n-1, k]/f[n, k]], {k, 8}];
Table[a[n], {n, 2, 70}] (* modified by G. C. Greubel, Mar 27 2022 *)
PROG
(Sage)
@CachedFunction
def b(n): # A004001
if (n<3): return 1
else: return b(b(n-1)) + b(n-b(n-1))
def f(n, k): return product( b(j) for j in (1..(n//2^k)) )
def A088493(n): return sum( (n*f(n-1, k)//f(n, k)) for k in (1..8) )
[A088493(n) for n in (2..70)] # G. C. Greubel, Mar 27 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Roger L. Bagula, Nov 10 2003
EXTENSIONS
Edited by G. C. Greubel, Mar 27 2022
STATUS
approved