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A098641 Number of partitions of the n-th Fibonacci number into Fibonacci numbers.

%I A098641 #16 Sep 20 2018 19:49:12
%S A098641 1,1,1,2,3,6,14,41,157,803,5564,53384,718844,13783708,380676448,
%T A098641 15298907733,902438020514,78720750045598,10220860796171917,
%U A098641 1986422867300209784,580763241873718042562,256553744608217295298827,171912553856721407543178940,175350753369071026461010505478
%N A098641 Number of partitions of the n-th Fibonacci number into Fibonacci numbers.
%C A098641 a(n) = A003107(A000045(n)).
%H A098641 Alois P. Heinz, <a href="/A098641/b098641.txt">Table of n, a(n) for n = 0..27</a>
%F A098641 a(n) = A098642(n) + A098643(n) + A098644(n).
%e A098641 n=6: A000045(6)=8, a(6) = #{8, 5+3, 5+2+1, 5+1+1+1, 3+3+2, 3+3+1+1, 3+2+2+1, 3+2+1+1+1, 3+1+1+1+1+1, 2+2+2+2, 2+2+2+1+1, 2+2+1+1+1+1, 2+1+1+1+1+1+1, 1+1+1+1+1+1+1+1} = 14; the other partitions of 8 into parts with at least one non-Fibonacci number: 7+1, 6+2, 6+1+1, 4+4, 4+3+1, 4+2+2, 4+2+1+1 and 4+1+1+1+1.
%t A098641 cl = CoefficientList[ Series[1/Product[(1 - x^Fibonacci[i]), {i, 2, 21}], {x, 0, 10950}], x]; cl[[ Table[ Fibonacci[i] + 1, {i, 21}] ]] (* _Robert G. Wilson v_, Apr 25 2005 *)
%Y A098641 Cf. A000041, A000045, A065033, A072214, A098642, A098643, A098644, A319503.
%K A098641 nonn
%O A098641 0,4
%A A098641 Marcel Dubois de Cadouin (dubois.ml(AT)club-internet.fr), Oct 27 2004
%E A098641 Corrected and extended by _Reinhard Zumkeller_, Apr 24 2005
%E A098641 a(15)-a(21) from _Robert G. Wilson v_, Apr 25 2005
%E A098641 Entry revised by _N. J. A. Sloane_, Mar 29 2006
%E A098641 a(0), a(22)-a(23) from _Alois P. Heinz_, Sep 20 2018