A056536 Mapping from half-antidiagonal reading of the triangle (as used in A028297) to the column-by-column reading of the triangular tables.

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, 38, 31, 25, 20, 56, 47, 39, 32, 26, 21, 67, 57, 48, 40, 33, 27, 79, 68, 58, 49, 41, 34, 28, 92, 80, 69, 59, 50, 42, 35, 106, 93, 81, 70, 60, 51, 43, 36, 121, 107, 94, 82, 71, 61, 52

Offset: 1

Author

Antti Karttunen, Jun 20 2000

Keywords

• nonn

Comments

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

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

Examples

			As a triangular array read by rows:
    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, 38, 31, 25, 20;
   56, 47, 39, 32, 26, 21;
   67, 57, 48, 40, 33, 27;
   79, 68, 58, 49, 41, 34, 28;
   92, 80, 69, 59, 50, 42, 35;
  106, 93, 81, 70, 60, 51, 43, 36;
  ...
		

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

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

Programs

Maple

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;

Formula

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

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