A358503 Positions inventory sequence: for stage k >= 2 we record where all the numbers from the two previous stages have appeared, starting with a(0) = 0, a(1) = 0.

0, 0, 0, 1, 1, 2, 3, 2, 3, 4, 5, 6, 4, 5, 7, 6, 8, 9, 10, 11, 7, 8, 9, 12, 10, 13, 11, 15, 14, 16, 17, 18, 19, 12, 13, 15, 14, 20, 16, 21, 17, 22, 18, 24, 19, 26, 23, 25, 28, 27, 29, 30, 31, 32, 20, 21, 22, 24, 26, 23, 33, 25, 34, 28, 36, 27, 35, 29, 38, 30, 40, 31, 42

Offset: 0

Author

Ctibor O. Zizka, Nov 21 2022

Keywords

• nonn
• tabf

Comments

When the sequence is displayed as a triangle, the row corresponding to stage k >= 2 is a permutation of the numbers from Fibonacci(k) - 1 to Fibonacci(k+2) - 2.

Examples

			As an irregular triangle, the sequence begins:
  0;
  0;
  0,  1;
  1,  2,  3;
  2,  3,  4,  5,  6;
  4,  5,  7,  6,  8,  9, 10, 11;
  7,  8,  9, 12, 10, 13, 11, 15, 14, 16, 17, 18, 19;
  ...
At stage 5 we look at two previous stages 3 and 4 and see the
positions of 1's: 4;
positions of 2's: 5, 7;
positions of 3's: 6, 8;
positions of 4's: 9;
positions of 5's: 10;
positions of 6's: 11;
thus stage 5 is 4, 5, 7, 6, 8, 9, 10, 11.
		

Crossrefs

Cf. A000045, A000071, A001911, A356784, A357317, A357443.