A358090 - OEIS

%I #18 Nov 03 2022 10:06:47

%S 1,1,1,2,1,2,3,1,3,2,4,5,1,4,2,6,3,5,7,8,1,6,3,8,2,10,4,7,5,11,9,12,

%T 13,1,9,3,13,5,11,2,15,6,17,4,10,7,16,8,12,19,14,18,20,21,1,14,5,20,3,

%U 16,7,24,9,18,2,22,8,26,4,28,11,15,6,25,10,19,12,29,13,17,31,21,27,23,32,30,33,34

%N 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-2 and n-1 flattened.

%C This sequence is a variant of A356784; here we consider two prior rows, there all prior rows, hence the term "partial" in the name.

%C The n-th row contains A000045(n) terms, and is a permutation of 1..A000045(n).

%H Rémy Sigrist, <a href="/A358090/b358090.txt">Table of n, a(n) for n = 1..10945</a>

%H Rémy Sigrist, <a href="/A358090/a358090.png">Scatterplot of the first 832039 terms</a>

%H Rémy Sigrist, <a href="/A358090/a358090.gp.txt">PARI program</a>

%F T(n, 1) = 1.

%F T(n, 2) = A001611(n-2) for n > 2.

%e Table begins:

%e     1,

%e     1,

%e     1, 2,

%e     1, 2, 3,

%e     1, 3, 2, 4, 5,

%e     1, 4, 2, 6, 3, 5, 7, 8,

%e     1, 6, 3, 8, 2, 10, 4, 7, 5, 11, 9, 12, 13,

%e     ...

%e For n = 7:

%e - the terms in rows 5 and 6 are: 1, 3, 2, 4, 5, 1, 4, 2, 6, 3, 5, 7, 8,

%e - positions of 1's are: 1, 6,

%e - positions of 2's are: 3, 8,

%e - positions of 3's are: 2, 10,

%e - positions of 4's are: 4, 7,

%e - positions of 5's are: 5, 11,

%e - positions of 6's are: 9,

%e - positions of 7's are: 12,

%e - positions of 8's are: 13,

%e - so row 7 is: 1, 6, 3, 8, 2, 10, 4, 7, 5, 11, 9, 12, 13.

%o (PARI) See Links section.

%Y See A358120 for a similar sequence.

%Y Cf. A000045, A001611, A342585, A356784, A358123.

%K nonn,tabf

%O 1,4

%A _Rémy Sigrist_, Oct 30 2022