A359010 - OEIS

%I #16 Dec 26 2022 15:48:47

%S 0,1,0,1,4,0,1,0,3,4,0,1,2,0,4,0,2,2,6,4,0,2,0,0,12,0,3,2,0,8,5,0,4,2,

%T 0,4,0,12,0,3,2,3,8,0,6,7,0,2,6,3,4,5,0,7,8,0,0,6,3,8,0,6,7,8,0,0,4,3,

%U 4,10,0,7,8,9,0,2,4,0,8,5,0,14,0,9,10,0

%N Variant of the inventory sequence: Record the number of terms whose value occurs once thus far in the sequence, then the number of terms whose value occurs twice thus far, and so on; a row ends when a 0 that would repeat infinitely is reached.

%C Note that we are counting terms with repetition. For example, to find a(5)=4, we are looking for the number of terms that appear twice. 0 and 1 each occur twice, which is 2+2=4 (not 1+1=2). This means that each column contains only multiples of the number of occurences it is counting.

%e First few rows of irregular triangle:

%e   0;

%e   1,  0;

%e   1,  4,  0;

%e   1,  0,  3,  4,  0;

%e   1,  2,  0,  4,  0;

%e   2,  2,  6,  4,  0;

%e   2,  0,  0, 12,  0;

%e   3,  2,  0,  8,  5,  0;

%e   4,  2,  0,  4,  0, 12,  0;

%e   3,  2,  3,  8,  0,  6,  7,  0;

%e   2,  6,  3,  4,  5,  0,  7,  8,  0;

%Y Cf. A342585, A350768.

%K nonn,tabf

%O 1,5

%A _Neal Gersh Tolunsky_, Dec 11 2022