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

1,2

Comments

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

Links

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

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

Example

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;
  ...

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 *)

Crossrefs

Cf. A135839, A024206.

Sequence in context: A141294 A174557 A010766 * A210992 A220484 A174066

Adjacent sequences: A135838 A135839 A135840 * A135842 A135843 A135844

Keyword

nonn,tabl

Author

Gary W. Adamson, Dec 01 2007

Extensions

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

Status

approved