%I #27 Dec 15 2023 10:58:14

%S 1,2,4,3,7,5,11,8,6,16,12,9,22,17,13,10,29,23,18,14,37,30,24,19,15,46,

%T 38,31,25,20,56,47,39,32,26,21,67,57,48,40,33,27,79,68,58,49,41,34,28,

%U 92,80,69,59,50,42,35,106,93,81,70,60,51,43,36,121,107,94,82,71,61,52

%N Mapping from half-antidiagonal reading of the triangle (as used in A028297) to the column-by-column reading of the triangular tables.

%C Moves squares (A000290) to triangular numbers (A000217). See 1st formula.

%C This sequence may be regarded as a triangular array read by rows: 1; 2; 4, 3; 7, 5; 11, 8, 6; 16, 12, 9; 22, 17, 13, 10; .... with row sums: A079824 = [1, 2, 7, 12, 25, 37, 62, 84, ...]. - _Philippe Deléham_, Feb 16 2004

%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>

%F a(A000290(i)) = A000217(i) for all i >= 1.

%F a(n) = A091018(n-1) + 1.

%e As a triangular array read by rows:

%e 1;

%e 2;

%e 4, 3;

%e 7, 5;

%e 11, 8, 6;

%e 16, 12, 9;

%e 22, 17, 13, 10;

%e 29, 23, 18, 14;

%e 37, 30, 24, 19, 15;

%e 46, 38, 31, 25, 20;

%e 56, 47, 39, 32, 26, 21;

%e 67, 57, 48, 40, 33, 27;

%e 79, 68, 58, 49, 41, 34, 28;

%e 92, 80, 69, 59, 50, 42, 35;

%e 106, 93, 81, 70, 60, 51, 43, 36;

%e ...

%p triang_perm := proc(upto_d) local a,i,j; a := []; for i from 1 to upto_d do for j from 1 to floor((i+1)/2) do a := [op(a),binomial((i-j)+1,2)+j]; od; od; RETURN(a); end;

%Y Cf. A000217, A000290, A056537 (inverse), A079824, A091018.

%K nonn

%O 1,2

%A _Antti Karttunen_, Jun 20 2000