A106314 Triangle T(n,k) composed of the squares min(n,k)^2.

1, 1, 1, 1, 4, 1, 1, 4, 4, 1, 1, 4, 9, 4, 1, 1, 4, 9, 9, 4, 1, 1, 4, 9, 16, 9, 4, 1, 1, 4, 9, 16, 16, 9, 4, 1, 1, 4, 9, 16, 25, 16, 9, 4, 1, 1, 4, 9, 16, 25, 25, 16, 9, 4, 1

Offset: 1

Author

Gary W. Adamson, Apr 28 2005

Keywords

• nonn
• tabl
• easy

Examples

			Replacing each term in A003983 by its square, we get:
{1},
{1, 1},
{1, 4, 1},
{1, 4, 4, 1},
{1, 4, 9, 4, 1},
{1, 4, 9, 9, 4, 1},
{1, 4, 9, 16, 9, 4, 1},
{1, 4, 9, 16, 16, 9, 4, 1},
{1, 4, 9, 16, 25, 16, 9, 4, 1},
{1, 4, 9, 16, 25, 25, 16, 9, 4, 1},
{1, 4, 9, 16, 25, 36, 25, 16, 9, 4, 1}
		

Crossrefs

Cf. A003983, A106314, A005993 (row sums).

Programs

Mathematica

Clear[p, n, i];
p[x_, n_] = Sum[x^i*If[i ==Floor[n/2] && Mod[n, 2] == 0, 0, If[i <= Floor[n/2], 2*i + 1, -(2*(n - i) + 1)]], {i, 0, n}]/(1 - x);
Table[CoefficientList[FullSimplify[p[x, n]], x], {n, 1, 11}];
Flatten[%]

Formula

T(n,k) = A003983(n,k)^2.

Extensions

Additional comments from Roger L. Bagula and Gary W. Adamson, Apr 02 2009