A128117 -id:A128117 - cp's OEIS frontend

A128118 At the n-th iteration the sequence of integers from n down to 1 are appended to the sequence a(n) times.

1, 2, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 7, 6, 5, 4, 3, 2, 1, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 9, 8, 7, 6, 5, 4, 3, 2, 1, 10, 9, 8, 7, 6, 5, 4, 3

Offset: 1

Reed Kelly, Feb 15 2007

			a(4) = 2 so 4,3,2,1,4,3,2,1 is added to the end of the sequence at the fourth iteration.

Reed Kelly, Feb 15 2007, Table of n, a(n) for n = 1..555

Cf. A128117, A001462, A002260.

crr[n_] := Module[ { A = {1,2,1,2,1}, i, j }, For [ i = 3, i <= n, i++, A = Join[ A, Flatten[ Table[ Range[i,1,-1], {A[[i]]} ]]]; ]; A ]

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.

Original entry on oeis.org

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

Rémy Sigrist, Feb 09 2022

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.

			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

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

Cf. A001462, A128117.

a:= proc() local k, l: k, l:= 3, [1$2, 2];
      proc(n)
        while nops(l)Alois P. Heinz, Feb 13 2022

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

cp's OEIS Frontend

A128118 At the n-th iteration the sequence of integers from n down to 1 are appended to the sequence a(n) times.

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