A095873 Triangle T(n,k) = (2*k-1)*(n+k-1)*(n-k+1) read by rows, 1<=k<=n.

1, 4, 9, 9, 24, 25, 16, 45, 60, 49, 25, 72, 105, 112, 81, 36, 105, 160, 189, 180, 121, 49, 144, 225, 280, 297, 264, 169, 64, 189, 300, 385, 432, 429, 364, 225, 81, 240, 385, 504, 585, 616, 585, 480, 289, 100, 297, 480, 637, 756, 825

Offset: 1

Author

Gary W. Adamson, Jun 10 2004

Keywords

• nonn
• tabl
• easy

Comments

Matrix square of A158405.

Examples

			[1 0 0 / 1 3 0 / 1 3 5]^2 = [1 0 0 / 4 9 0 / 9 24 25]. Delete the zeros and
read by rows:
1;
4, 9;
9, 24, 25;
16,45, 60, 49;
25,72,105,112, 81;
		

References

• Albert H. Beiler, "Recreations in the Theory of Numbers", Dover, 1966.

Crossrefs

Cf. A094728, A095871, A095872.

Programs

Maple

A095873 := proc(n,k)
        (2*k-1)*(n+k-1)*(n-k+1) ;
end proc:
seq(seq(A095873(n,k),k=1..n),n=1..13) ; # R. J. Mathar, Oct 30 2011

Mathematica

Table[(2k-1)(n+k-1)(n-k+1),{n,10},{k,n}]//Flatten (* Harvey P. Dale, May 03 2018 *)

Formula

T(n,k) = (2*k-1)*A094728(n,k).

Sum_{k=1..n} T(n,k)= n*(n+1)*(3*n^2+n-1)/6 = A103220(n). - R. J. Mathar, Oct 30 2011

Extensions

Definition in closed form by R. J. Mathar, Oct 30 2011