A152204 Triangle read by rows: T(n,k) = 2*n-4*k+5 (n >= 0, 1 <= k <= 1+floor(n/2)).

1, 3, 5, 1, 7, 3, 9, 5, 1, 11, 7, 3, 13, 9, 5, 1, 15, 11, 7, 3, 17, 13, 9, 5, 1, 19, 15, 11, 7, 3, 21, 17, 13, 9, 5, 1, 23, 19, 15, 11, 7, 3, 25, 21, 17, 13, 9, 5, 1, 27, 23, 19, 15, 11, 7, 3, 29, 25, 21, 17, 13, 9, 5, 1, 31, 27, 23, 19, 15, 11, 7, 3, 33

Offset: 0

Author

Gary W. Adamson, Nov 29 2008

Keywords

• nonn
• tabf
• easy

Comments

All terms are odd, decreasing across rows. Row sums = A000217, the triangular numbers.

From Johannes W. Meijer, Sep 08 2013: (Start)

Triangle read by rows formed from the antidiagonals of triangle A099375.

The alternating row sums equal A098181(n). (End)

Examples

			First few rows of the triangle:
  1
  3
  5  1
  7  3
  9  5  1
  11 7  3
  13 9  5  1
  15 11 7  3
  17 13 9  5 1
  19 15 11 7 3
  21 17 13 9 5 1
  ...
		

Links

• Nathaniel Johnston, Rows n = 0..200 of irregular triangle, flattened

Crossrefs

Cf. A000217.

Programs

Maple

T := proc(n,k) return 2*n-4*k+5: end: seq(seq(T(n,k), k=1..1+floor(n/2)), n=0..20); # Nathaniel Johnston, May 01 2011

Formula

By columns, odd terms in every column, n-th column starts at row (2*n).

From Johannes W. Meijer, Sep 08 2013: (Start)

T(n, k) = A099375(n-k+1, k-1), n >= 0 and 1 <= k <= 1+floor(n/2).

T(n, k) = A158405(n+1, n-2*k+2). (End)

Extensions

Edited by N. J. A. Sloane, Sep 25 2010, following a suggestion from Emeric Deutsch

Offset corrected by Johannes W. Meijer, Sep 07 2013