A183090 Tree generated by A005652, associated with numbers which are not the sum of two Fibonacci numbers.

1, 2, 3, 4, 6, 5, 8, 7, 11, 12, 9, 10, 16, 15, 14, 13, 21, 23, 22, 25, 17, 18, 19, 20, 30, 33, 29, 31, 27, 28, 24, 26, 42, 41, 45, 46, 43, 44, 50, 49, 32, 34, 35, 36, 37, 38, 40, 39, 58, 60, 64, 67, 56, 59, 61, 62, 53, 54, 55, 57, 48, 47, 51, 52

Offset: 1

Author

Clark Kimberling, Dec 24 2010

Keywords

• nonn
• tabf

Comments

A permutation of the positive integers. See the comment at A183079.

Examples

			Top 5 rows:
  1;
  2;
  3,             4;
  6,      5,     8,      7;
  11, 12, 9, 10, 16, 15, 14, 13;
From row 3 to row 4: 3->(6,5) and 4->(8,7). For all such pairs, the 1st component is in L and the 2nd, in U.
		

Crossrefs

Cf. A005652, A005653, A183079, A074049.

Formula

Let L(n)=A005652(n) and U(n)=A005653(n), these being complementary sequences, each comprising a maximal set no two of whose elements is a Fibonacci number.

The tree-array T(n,k) is then given by rows:

T(0,0)=1; T(1,0)=2;

T(n,2*j)=L(T(n-1,j));

T(n,2*j+1)=U(T(n-1,j));

for j=0,1,...,2^(n-1)-1, n>=2.