A143971 Triangle read by rows, (3n-2) subsequences decrescendo.

1, 4, 1, 7, 4, 1, 10, 7, 4, 1, 13, 10, 7, 4, 1, 16, 13, 10, 7, 4, 1, 19, 16, 13, 10, 7, 4, 1, 22, 19, 16, 13, 10, 7, 4, 1, 25, 22, 19, 16, 13, 10, 7, 4, 1, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1, 31, 28, 25, 22, 19, 16, 13, 10, 7, 4, 1

Offset: 1

Author

Gary W. Adamson, Sep 06 2008

Keywords

• nonn
• tabl

Comments

Row sums = pentagonal numbers, A000326: (1, 5, 12, 22, 35,...).

The alternating row sums lead to A032766 and the antidiagonal sums to A006578. - Johannes W. Meijer, Sep 05 2013

Examples

			Triangle starts
1;
4, 1;
7, 4, 1;
10, 7, 4, 1;
...
		

Crossrefs

Cf. A016777, A000326, A209634.

Programs

Maple

T := (n, k) -> 3*n-3*k+1: seq(seq(T(n, k), k=1..n), n=1..11); # Johannes W. Meijer, Sep 05 2013

Formula

Triangle read by rows, (3n-2) subsequences decrescendo; 1<=k<=n.

(1, 4, 7, 10, 13,...) in every column.

T(n,k) = 3*n - 3*k + 1.

Extensions

Terms a(17) and a(38) corrected and terms added by Johannes W. Meijer, Sep 05 2013