%I #40 Oct 31 2022 06:00:26

%S 0,1,0,0,3,0,0,2,3,1,1,1,5,0,0,2,3,5,6,4,1,1,9,10,11,1,2,7,2,3,4,8,7,

%T 0,0,2,3,5,6,13,14,7,1,1,9,10,11,20,21,25,4,2,7,15,26,28,4,3,4,8,16,

%U 29,2,4,19,30,2,5,12,17,1,6,18,1,7,27,1,8,31,1,9,22,1,10,23,1,11,24,9,0,0,2,3

%N Inventory count sequence: record what you see and where it is located.

%C To get started we set a(0)=0. Now start with zero terms. We record ONE ZERO at position ZERO. The sequence is now 0,1,0,0. Now start again with zero terms. We record THREE ZEROS at positions 0,2,3. Next start with one terms. We record ONE ONE at position ONE. The sequence is now 0,1,0,0,3,0,0,2,3,1,1,1. Now start again with zero terms...one terms...two terms...three terms. The sequence is now 0,1,...,2,3,4,8. And so on.

%H Thomas Scheuerle, <a href="/A357317/b357317.txt">Table of n, a(n) for n = 0..4895</a>

%H Thomas Scheuerle, <a href="/A357317/a357317.png">a(0..10000) as scatter plot</a>

%e a(0) = 0

%e counting over a(0):

%e a(1) = 1, a(2) = 0, a(3) = 0 (count one zero at position 0)

%e counting over a(0)..a(3):

%e a(4) = 3, a(5) = 0, a(6) = 0, a(7) = 2, a(8) = 3, (count 3 zeros at positions 0,2,3)

%e a(9) = 1, a(10) = 1, a(11) = 1 (count 1 one at position 1)

%e counting over a(0)..a(11):

%e a(12) = 5, a(13) = 0, a(14) = 0, a(15) = 2, a(16) = 3, a(17) = 5, a(18) = 6 (count 5 zeros at positions 0,2,3,5,6)

%e a(19) = 4, a(20) = 1, a(21) = 1, a(22) = 9, a(23) = 10, a(24) = 11 (count 4 ones at positions 1,9,10,11)

%e a(25) = 1, a(26) = 2, a(27) = 7 (count 1 two at position 7)

%e a(28) = 2, a(29) = 3, a(30) = 4, a(31) = 8 (count 2 threes at positions 4,8)

%e counting over a(0)..a(31):

%e etc.

%o (MATLAB)

%o function a = A357317( min_length )

%o a = 0;

%o while length(a) < min_length

%o b = a; c = unique(a);

%o for m = 1:length(c)

%o nextnumber = c(m);

%o indices = find(a == nextnumber);

%o b = [b length(indices) nextnumber indices-1];

%o end

%o a = b;

%o end

%o end % _Thomas Scheuerle_, Sep 29 2022

%Y Cf. A342585.

%K nonn,look

%O 0,5

%A _Ctibor O. Zizka_, Sep 29 2022