A359010 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.

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

Offset

1,5

Comments

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.

Links

Table of n, a(n) for n=1..86.

Example

First few rows of irregular triangle:
  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,  0,  4,  0, 12,  0;
  3,  2,  3,  8,  0,  6,  7,  0;
  2,  6,  3,  4,  5,  0,  7,  8,  0;

Crossrefs

Cf. A342585, A350768.

Sequence in context: A136630 A275714 A111728 * A143784 A272774 A333274

Adjacent sequences: A359007 A359008 A359009 * A359011 A359012 A359013

Keyword

nonn,tabf

Author

Neal Gersh Tolunsky, Dec 11 2022

Status

approved