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A358120 Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-1 and n-2 flattened.

%I A358120 #15 Nov 03 2022 10:06:52
%S A358120 1,1,1,2,1,3,2,1,4,3,5,2,1,6,5,8,3,7,2,4,1,9,7,13,5,11,8,10,3,12,2,6,
%T A358120 4,1,14,11,20,9,18,13,21,5,16,12,15,3,19,7,17,2,8,6,10,4,1,22,17,32,
%U A358120 13,30,21,34,9,26,19,33,15,24,18,28,5,23,20,29,3,27,11,31,7,25,2,12,10,16,6,14,4,8
%N A358120 Partial inventory of positions as an irregular table; rows 1 and 2 contain 1, for n > 2, row n contains the 1-based positions of 1's, followed by the positions of 2's, 3's, etc. in rows n-1 and n-2 flattened.
%C A358120 The n-th row contains A000045(n) terms, and is a permutation of 1..A000045(n).
%H A358120 Rémy Sigrist, <a href="/A358120/b358120.txt">Table of n, a(n) for n = 1..10945</a>
%H A358120 Rémy Sigrist, <a href="/A358120/a358120.gp.txt">PARI program</a>
%H A358120 Rémy Sigrist, <a href="/A358120/a358120.png">Scatterplot of the first 832039 terms</a>
%F A358120 T(n, 1) = 1.
%F A358120 T(n, 2) = A001611(n-1) for n > 2.
%e A358120 Table begins:
%e A358120     1,
%e A358120     1,
%e A358120     1, 2,
%e A358120     1, 3, 2,
%e A358120     1, 4, 3, 5, 2,
%e A358120     1, 6, 5, 8, 3, 7, 2, 4,
%e A358120     1, 9, 7, 13, 5, 11, 8, 10, 3, 12, 2, 6, 4,
%e A358120     ...
%e A358120 For n = 7:
%e A358120 - terms in rows 6 and 5 are: 1, 6, 5, 8, 3, 7, 2, 4, 1, 4, 3, 5, 2,
%e A358120 - positions of 1's are: 1, 9,
%e A358120 - positions of 2's are: 7, 13,
%e A358120 - positions of 3's are: 5, 11,
%e A358120 - positions of 4's are: 8, 10,
%e A358120 - positions of 5's are: 3, 12,
%e A358120 - positions of 6's are: 2,
%e A358120 - positions of 7's are: 6,
%e A358120 - positions of 8's are: 4,
%e A358120 - so row 7 is: 1, 9, 7, 13, 5, 11, 8, 10, 3, 12, 2, 6, 4.
%o A358120 (PARI) See Links section.
%Y A358120 See A358090 for a similar sequence.
%Y A358120 Cf. A000045, A001611, A342585, A356784, A358124.
%K A358120 nonn,tabf
%O A358120 1,4
%A A358120 _Rémy Sigrist_, Oct 30 2022