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A273156 Product of all parts in Zeckendorf representation of n.

%I A273156 #23 May 18 2016 00:45:04
%S A273156 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 A273156 63,105,105,210,168,168,336,504,504,34,34,68,102,102,170,170,340,272,
%U A273156 272,544,816,816,442,442,884,1326,1326,2210,2210,4420,55,55,110,165
%N A273156 Product of all parts in Zeckendorf representation of n.
%H A273156 Peter Kagey, <a href="/A273156/b273156.txt">Table of n, a(n) for n = 0..10000</a>
%H A273156 StackExchange user "orlp", <a href="http://codegolf.stackexchange.com/questions/79854">Fibonacci products</a>.
%e A273156 a(33) = 21*8*3*1 because 33 = 21+8+3+1.
%p A273156 A273156 := proc(n)
%p A273156     local nred,a,f ;
%p A273156     if n = 0 then
%p A273156         0;
%p A273156     else
%p A273156         nred := n ;
%p A273156         a := 1 ;
%p A273156         while nred > 1 do
%p A273156             f := A087172(nred) ;
%p A273156             a := a*f ;
%p A273156             nred := nred-f ;
%p A273156         end do:
%p A273156         a ;
%p A273156     end if;
%p A273156 end proc: # _R. J. Mathar_, May 17 2016
%t A273156 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 A273156 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 A273156 (Haskell)
%o A273156 a273156 = product . a035516_row
%Y A273156 Cf. A035516, A106530.
%K A273156 nonn,look
%O A273156 0,3
%A A273156 _Peter Kagey_, May 16 2016