A135840 A135839 * A000012 as infinite lower triangular matrices.

1, 2, 1, 2, 1, 1, 3, 2, 1, 1, 3, 2, 2, 1, 1, 4, 3, 2, 2, 1, 1, 4, 3, 3, 2, 2, 1, 1, 5, 4, 3, 3, 2, 2, 1, 1, 5, 4, 4, 3, 3, 2, 2, 1, 1, 6, 5, 4, 4, 3, 3, 2, 2, 1, 1, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 7, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1, 8, 7, 6, 6, 5, 5, 4, 4, 3, 3, 2, 2, 1, 1

Offset: 1

Author

Gary W. Adamson, Dec 01 2007

Keywords

• nonn

Comments

Row sums = A004652 starting (1, 3, 4, 7, 9, 13, 16, 21, ...).

Examples

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

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows

Crossrefs

Cf. A135839, A004652, A135841.

Programs

Mathematica

T[1, 1] := 1; T[n_, 1] := Floor[(n + 2)/2]; T[n_, n_] := 1; T[n_, k_] := Floor[(n - k + 2)/2]; Table[T[n, k], {n, 1, 8}, {k, 1, n}]//Flatten (* G. C. Greubel, Dec 05 2016 *)

Formula

T(1, 1) = 1, T(n, 1) = floor((n + 2)/2), T(n, n) = 1, T(n, k) = floor((n - k + 2)/2). - G. C. Greubel, Dec 05 2016