cp's OEIS Frontend

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.

%I A358503 #35 Nov 22 2022 22:18:09
%S A358503 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,
%T A358503 17,18,19,12,13,15,14,20,16,21,17,22,18,24,19,26,23,25,28,27,29,30,31,
%U A358503 32,20,21,22,24,26,23,33,25,34,28,36,27,35,29,38,30,40,31,42
%N 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.
%C A358503 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.
%e A358503 As an irregular triangle, the sequence begins:
%e A358503   0;
%e A358503   0;
%e A358503   0,  1;
%e A358503   1,  2,  3;
%e A358503   2,  3,  4,  5,  6;
%e A358503   4,  5,  7,  6,  8,  9, 10, 11;
%e A358503   7,  8,  9, 12, 10, 13, 11, 15, 14, 16, 17, 18, 19;
%e A358503   ...
%e A358503 At stage 5 we look at two previous stages 3 and 4 and see the
%e A358503 positions of 1's: 4;
%e A358503 positions of 2's: 5, 7;
%e A358503 positions of 3's: 6, 8;
%e A358503 positions of 4's: 9;
%e A358503 positions of 5's: 10;
%e A358503 positions of 6's: 11;
%e A358503 thus stage 5 is 4, 5, 7, 6, 8, 9, 10, 11.
%Y A358503 Cf. A000045, A000071, A001911, A356784, A357317, A357443.
%K A358503 nonn,tabf
%O A358503 0,6
%A A358503 _Ctibor O. Zizka_, Nov 21 2022