A135841 A000012 * A135839 as infinite lower triangular matrices.

1, 2, 1, 3, 1, 1, 4, 2, 1, 1, 5, 2, 2, 1, 1, 6, 3, 2, 2, 1, 1, 7, 3, 3, 2, 2, 1, 1, 8, 4, 3, 3, 2, 2, 1, 1, 9, 4, 4, 3, 3, 2, 2, 1, 1, 10, 5, 4, 4, 3, 3, 2, 2, 1, 1, 11, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 12, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 13, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1

Offset: 1

Author

Gary W. Adamson, Dec 01 2007

Keywords

• nonn
• tabl

Comments

Row sums = A024206: (1, 3, 5, 8, 11, 15, 19, ...).

Examples

			First few rows of the triangle:
  1;
  2, 1;
  3, 1, 1;
  4, 2, 1, 1;
  5, 2, 2, 1, 1;
  6, 3, 2, 2, 1, 1;
  7, 3, 3, 2, 2, 1, 1;
  ...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1275

Crossrefs

Cf. A135839, A024206.

Programs

Mathematica

T[1, 1] := 1; T[n_, 1] := n; T[n_, n_] := 1; T[n_, k_] := Floor[(n - k + 2)/2]; Table[T[n, k], {n, 1, 15}, {k, 1, n}]//Flatten (* G. C. Greubel, Dec 06 2016 *)

Formula

T(1, 1) = 1, T(n, 1) = n, T(n, n) = 1, T(n, k) = floor((n - k + 2)/2). - G. C. Greubel, Dec 06 2016

Extensions

Terms a(56) and beyond from G. C. Greubel, Dec 06 2016