A140829 a(0)=1; for n >= 1, a(n) = ceiling(Fibonacci(n)/a(n-1)).

1, 1, 1, 2, 2, 3, 3, 5, 5, 7, 8, 12, 12, 20, 19, 33, 30, 54, 48, 88, 77, 143, 124, 232, 200, 376, 323, 609, 522, 986, 844, 1596, 1365, 2583, 2208, 4180, 3572, 6764, 5779, 10945, 9350, 17710, 15128, 28656, 24477, 46367, 39604, 75024, 64080, 121392, 103683

Offset

0,4

Links

Table of n, a(n) for n=0..50.

Formula

Conjectures from Colin Barker, Mar 08 2019: (Start)

G.f.: (1 + x + x^3)*(1 + x - x^9) / ((1 + x)*(1 - x^2 - x^4)).

a(n) = -a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) for n>12.

(End)

Maple

with(combinat): a:=proc(n) if n=0 then 1 else ceil(fibonacci(n)/a(n-1)) end if end proc: seq(a(n), n=0..50); # Emeric Deutsch, Aug 09 2008

Mathematica

RecurrenceTable[{a[0]==1, a[n]==Ceiling[Fibonacci[n]/a[n-1]]}, a, {n, 50}] (* Harvey P. Dale, Dec 13 2013 *)

Crossrefs

Cf. A140828 (similar sequence).

Sequence in context: A008484 A274146 A027189 * A346523 A184324 A274168

Adjacent sequences: A140826 A140827 A140828 * A140830 A140831 A140832

Keyword

nonn

Author

Leroy Quet, Jul 18 2008

Extensions

More terms from Emeric Deutsch, Aug 09 2008

Status

approved