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%I #23 May 18 2016 00:45:04
%S 0,1,2,3,3,5,5,10,8,8,16,24,24,13,13,26,39,39,65,65,130,21,21,42,63,
%T 63,105,105,210,168,168,336,504,504,34,34,68,102,102,170,170,340,272,
%U 272,544,816,816,442,442,884,1326,1326,2210,2210,4420,55,55,110,165
%N Product of all parts in Zeckendorf representation of n.
%H Peter Kagey, <a href="/A273156/b273156.txt">Table of n, a(n) for n = 0..10000</a>
%H StackExchange user "orlp", <a href="http://codegolf.stackexchange.com/questions/79854">Fibonacci products</a>.
%e a(33) = 21*8*3*1 because 33 = 21+8+3+1.
%p A273156 := proc(n)
%p local nred,a,f ;
%p if n = 0 then
%p 0;
%p else
%p nred := n ;
%p a := 1 ;
%p while nred > 1 do
%p f := A087172(nred) ;
%p a := a*f ;
%p nred := nred-f ;
%p end do:
%p a ;
%p end if;
%p end proc: # _R. J. Mathar_, May 17 2016
%t t = Fibonacci /@ Range@ 21; {0}~Join~Table[Times @@ If[MemberQ[t, n], {n}, Most@ MapAt[# + 1 &, Abs@ Differences@ FixedPointList[# - First@ Reverse@ TakeWhile[t, Function[k, # >= k]] &, n], -1]], {n, 58}] (* _Michael De Vlieger_, May 17 2016 *)
%t a[0]=0; a[n_]:=Block[{m=n, p=1, f, k=0}, While[Fibonacci@ ++k <= n]; While[ m>1, f= Fibonacci@ --k; If[ f<=m, m-=f; p*=f]]; p]; Array[a, 80, 0] (* _Giovanni Resta_, May 17 2016 *)
%o (Haskell)
%o a273156 = product . a035516_row
%Y Cf. A035516, A106530.
%K nonn,look
%O 0,3
%A _Peter Kagey_, May 16 2016
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