A035516 -id:A035516 - cp's OEIS frontend

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

Peter Kagey, May 16 2016

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

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

Cf. A035516, A106530.

Haskell
```
a273156 = product . a035516_row
```

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

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 *)

A107227 Numbers having no odd terms in their Zeckendorf representation.

Original entry on oeis.org

2, 8, 10, 34, 36, 42, 44, 144, 146, 152, 154, 178, 180, 186, 188, 610, 612, 618, 620, 644, 646, 652, 654, 754, 756, 762, 764, 788, 790, 796, 798, 2584, 2586, 2592, 2594, 2618, 2620, 2626, 2628, 2728, 2730, 2736, 2738, 2762, 2764, 2770, 2772, 3194, 3196, 3202

Offset: 1

Reinhard Zumkeller, May 15 2005

nonn

A107016(a(n))=0, A107015(a(n))>0; subsequence of A107225.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Zeckendorf Representation

Cf. A107228.

Cf. A035516, A014437, A014445, A011655.

a107227 n = a107227_list !! (n-1)
a107227_list = filter ((all even) . a035516_row) [1..]
-- Reinhard Zumkeller, Mar 10 2013

A107228 Numbers having no even terms in their Zeckendorf representation.

Original entry on oeis.org

1, 3, 4, 5, 6, 13, 14, 16, 17, 18, 19, 21, 22, 24, 25, 26, 27, 55, 56, 58, 59, 60, 61, 68, 69, 71, 72, 73, 74, 76, 77, 79, 80, 81, 82, 89, 90, 92, 93, 94, 95, 102, 103, 105, 106, 107, 108, 110, 111, 113, 114, 115, 116, 233, 234, 236, 237, 238, 239, 246, 247, 249, 250

Offset: 1

Reinhard Zumkeller, May 15 2005

nonn

A107015(a(n))=0, A107016(a(n))>0; subsequence of A107224.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Zeckendorf Representation

Cf. A107227.

Cf. A035516, A014437, A014445, A011655.

a107228 n = a107228_list !! (n-1)
a107228_list = filter ((all odd) . a035516_row) [1..]
-- Reinhard Zumkeller, Mar 10 2013

A357120 Irregular triangle T(n, k), n > 0, k = 1..A278043(n); the n-th row contains, in ascending order, the terms in the greedy tribonacci representation of n.

Original entry on oeis.org

1, 2, 1, 2, 4, 1, 4, 2, 4, 7, 1, 7, 2, 7, 1, 2, 7, 4, 7, 1, 4, 7, 13, 1, 13, 2, 13, 1, 2, 13, 4, 13, 1, 4, 13, 2, 4, 13, 7, 13, 1, 7, 13, 2, 7, 13, 1, 2, 7, 13, 24, 1, 24, 2, 24, 1, 2, 24, 4, 24, 1, 4, 24, 2, 4, 24, 7, 24, 1, 7, 24, 2, 7, 24, 1, 2, 7, 24, 4, 7, 24

Offset: 1

Rémy Sigrist, Sep 12 2022

See A357121 for the sequence corresponding to lazy tribonacci representations.

			Triangle T(n, k) begins:
     1: [1]
     2: [2]
     3: [1, 2]
     4: [4]
     5: [1, 4]
     6: [2, 4]
     7: [7]
     8: [1, 7]
     9: [2, 7]
    10: [1, 2, 7]
    11: [4, 7]
    12: [1, 4, 7]
    13: [13]
    14: [1, 13]
    15: [2, 13]

Rémy Sigrist, PARI program
Index entries for sequences related to Zeckendorf expansion of n

Cf. A000073, A035516, A035517, A275392, A278043, A278038, A357121.

PARI
```
See Links section.
```

T(n, 1) = A275392(n).

Sum_{k = 1..A278043(n)} T(n, k) = n.

cp's OEIS Frontend

A273156 Product of all parts in Zeckendorf representation of n.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Haskell

Maple

Mathematica

A107227 Numbers having no odd terms in their Zeckendorf representation.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

A107228 Numbers having no even terms in their Zeckendorf representation.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

A357120 Irregular triangle T(n, k), n > 0, k = 1..A278043(n); the n-th row contains, in ascending order, the terms in the greedy tribonacci representation of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula