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Triangular array: row n gives the positions of n+1 in A349946.
3

%I #12 Jun 05 2023 08:55:38

%S 1,2,4,3,5,9,6,7,10,16,8,11,12,17,25,13,14,18,19,26,36,15,20,21,27,28,

%T 37,49,22,23,29,30,38,39,50,64,24,31,32,40,41,51,52,65,81,33,34,42,43,

%U 53,54,66,67,82,100,35,44,45,55,56,68,69,83,84,101,121

%N Triangular array: row n gives the positions of n+1 in A349946.

%C Every positive integer occurs exactly once, so as a sequence, this is a permutation of the positive integers.

%C Row n ends in n^2. The first term in row n is (1 + n/1)^2 - 3 if n >= 4 and n is even; as in A028872(n) for n >= 3.

%C The first term in row n is ((n+1)/2)^2 - 1 if n >= 3 and n is odd, as in A132411(n) for n >= 3.

%e First 7 rows:

%e 1

%e 2 4

%e 3 5 9

%e 6 7 10 16

%e 8 11 12 17 25

%e 13 14 18 19 26 36

%e 14 20 21 27 28 37 49

%t t = {1, 1}; Do[t = Join[t, Riffle[Range[n], n], {n}], {n, 2, 100}];

%t u = Flatten[Partition[t, 2]];

%t v = Table[n (n + 1), {n, 1, 80}];

%t d = Delete[u, Map[{#} &, v]]; (* A349526 *)

%t p = Table[{d[[n]], d[[n + 1]]}, {n, 1, 150}];

%t q = Map[Total, p] (* A349946 *)

%t r = Table[Flatten[Position[q, n]], {n, 2, 12}] (* A349947 array *)

%t Flatten[r] (* A349947 sequence *)

%Y Cf. A349526, A349946.

%K nonn,tabl

%O 1,2

%A _Clark Kimberling_, Dec 07 2021