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

1,2

Comments

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

Links

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

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

Example

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;
  ...

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 *)

Crossrefs

Cf. A135839, A004652, A135841.

Sequence in context: A135539 A240060 A129264 * A228570 A173305 A233867

Adjacent sequences: A135837 A135838 A135839 * A135841 A135842 A135843

Keyword

nonn

Author

Gary W. Adamson, Dec 01 2007

Status

approved