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

0,3

Links

Peter Kagey, Table of n, a(n) for n = 0..10000

StackExchange user "orlp", Fibonacci products.

Example

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

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 *)

Prog

(Haskell)
a273156 = product . a035516_row

Crossrefs

Cf. A035516, A106530.

Sequence in context: A134408 A051032 A106530 * A294487 A212792 A281363

Adjacent sequences: A273153 A273154 A273155 * A273157 A273158 A273159

Keyword

nonn,look

Author

Peter Kagey, May 16 2016

Status

approved