A351192 Irregular table of positive integers read by rows; the n-th row contains a(n) 1's, a(n) 2's, ..., a(n) n's, in that order.

1, 1, 2, 1, 1, 2, 2, 3, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 9, 9, 9

Offset

1,3

Comments

This sequence is a variant of A128117.

The sequence is well defined:

- the first row must start with a value 1, so a(1) = 1, and the first row is (1),

- the second row must start with a value 1, so a(2) = 1, and the second row is (1, 2),

- subsequent rows are determined by terms in prior rows.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10256 (rows for n = 1..68 flattened)

Rémy Sigrist, Scatterplot of the terms in rows for n = 1..500

Example

The first terms and rows are:
  n   a(n)  n-th row
  --  ----  ----------------------------------------
   1     1  1
   2     1  1, 2
   3     2  1, 1, 2, 2, 3, 3
   4     1  1, 2, 3, 4
   5     1  1, 2, 3, 4, 5
   6     2  1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6
   7     2  1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7

Maple

a:= proc() local k, l: k, l:= 3, [1$2, 2];
      proc(n)
        while nops(l)<n do
          l, k:= [l[], seq(i$a(k), i=1..k)], k+1
        od: l[n]
      end
    end():
seq(a(n), n=1..95);  # Alois P. Heinz, Feb 13 2022

Prog

(PARI) a = vector(95, n, 1); m=0; for (n=1, 9, for (k=1, n, for (t=1, a[n], print1 (a[m++]=k", "))))

Crossrefs

Cf. A001462, A128117.

Sequence in context: A359384 A100480 A268811 * A306460 A317805 A231561

Adjacent sequences: A351189 A351190 A351191 * A351193 A351194 A351195

Keyword

nonn,look,tabf

Author

Rémy Sigrist, Feb 09 2022

Status

approved