A273156 Product of all parts in Zeckendorf representation of n.

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, 63, 105, 105, 210, 168, 168, 336, 504, 504, 34, 34, 68, 102, 102, 170, 170, 340, 272, 272, 544, 816, 816, 442, 442, 884, 1326, 1326, 2210, 2210, 4420, 55, 55, 110, 165

Offset: 0

Author

Peter Kagey, May 16 2016

Keywords

• nonn
• look

Examples

			a(33) = 21*8*3*1 because 33 = 21+8+3+1.
		

Links

• Peter Kagey, Table of n, a(n) for n = 0..10000
• StackExchange user "orlp", Fibonacci products.

Crossrefs

Cf. A035516, A106530.

Programs

Haskell

a273156 = product . a035516_row

Maple

A273156 := proc(n)
    local nred,a,f ;
    if n = 0 then
        0;
    else
        nred := n ;
        a := 1 ;
        while nred > 1 do
            f := A087172(nred) ;
            a := a*f ;
            nred := nred-f ;
        end do:
        a ;
    end if;
end proc: # R. J. Mathar, May 17 2016

Mathematica

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 *)
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 *)