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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.

%I A351192 #32 Feb 14 2022 13:37:23
%S A351192 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,
%T A351192 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,
%U A351192 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
%N 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.
%C A351192 This sequence is a variant of A128117.
%C A351192 The sequence is well defined:
%C A351192 - the first row must start with a value 1, so a(1) = 1, and the first row is (1),
%C A351192 - the second row must start with a value 1, so a(2) = 1, and the second row is (1, 2),
%C A351192 - subsequent rows are determined by terms in prior rows.
%H A351192 Rémy Sigrist, <a href="/A351192/b351192.txt">Table of n, a(n) for n = 1..10256</a> (rows for n = 1..68 flattened)
%H A351192 Rémy Sigrist, <a href="/A351192/a351192.png">Scatterplot of the terms in rows for n = 1..500</a>
%e A351192 The first terms and rows are:
%e A351192   n   a(n)  n-th row
%e A351192   --  ----  ----------------------------------------
%e A351192    1     1  1
%e A351192    2     1  1, 2
%e A351192    3     2  1, 1, 2, 2, 3, 3
%e A351192    4     1  1, 2, 3, 4
%e A351192    5     1  1, 2, 3, 4, 5
%e A351192    6     2  1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6
%e A351192    7     2  1, 1, 2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 7
%p A351192 a:= proc() local k, l: k, l:= 3, [1$2, 2];
%p A351192       proc(n)
%p A351192         while nops(l)<n do
%p A351192           l, k:= [l[], seq(i$a(k), i=1..k)], k+1
%p A351192         od: l[n]
%p A351192       end
%p A351192     end():
%p A351192 seq(a(n), n=1..95);  # _Alois P. Heinz_, Feb 13 2022
%o A351192 (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", "))))
%Y A351192 Cf. A001462, A128117.
%K A351192 nonn,look,tabf
%O A351192 1,3
%A A351192 _Rémy Sigrist_, Feb 09 2022