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%I A056536 #27 Dec 15 2023 10:58:14
%S A056536 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 A056536 38,31,25,20,56,47,39,32,26,21,67,57,48,40,33,27,79,68,58,49,41,34,28,
%U A056536 92,80,69,59,50,42,35,106,93,81,70,60,51,43,36,121,107,94,82,71,61,52
%N A056536 Mapping from half-antidiagonal reading of the triangle (as used in A028297) to the column-by-column reading of the triangular tables.
%C A056536 Moves squares (A000290) to triangular numbers (A000217). See 1st formula.
%C A056536 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 A056536 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A056536 a(A000290(i)) = A000217(i) for all i >= 1.
%F A056536 a(n) = A091018(n-1) + 1.
%e A056536 As a triangular array read by rows:
%e A056536     1;
%e A056536     2;
%e A056536     4,  3;
%e A056536     7,  5;
%e A056536    11,  8, 6;
%e A056536    16, 12, 9;
%e A056536    22, 17, 13, 10;
%e A056536    29, 23, 18, 14;
%e A056536    37, 30, 24, 19, 15;
%e A056536    46, 38, 31, 25, 20;
%e A056536    56, 47, 39, 32, 26, 21;
%e A056536    67, 57, 48, 40, 33, 27;
%e A056536    79, 68, 58, 49, 41, 34, 28;
%e A056536    92, 80, 69, 59, 50, 42, 35;
%e A056536   106, 93, 81, 70, 60, 51, 43, 36;
%e A056536   ...
%p A056536 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 A056536 Cf. A000217, A000290, A056537 (inverse), A079824, A091018.
%K A056536 nonn
%O A056536 1,2
%A A056536 _Antti Karttunen_, Jun 20 2000

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