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

1,2

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

Links

Table of n, a(n) for n=1..71.

Index entries for sequences that are permutations of the natural numbers

Formula

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

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

Example

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;
  ...

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;

Crossrefs

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

Sequence in context: A255128 A252460 A252752 * A258237 A361939 A371237

Adjacent sequences: A056533 A056534 A056535 * A056537 A056538 A056539

Keyword

nonn

Author

Antti Karttunen, Jun 20 2000

Status

approved