A214011 T(n,k) is the number of n X n nonnegative integer matrices with row and column i=1..n having sum <= i*k.

2, 3, 12, 4, 54, 271, 5, 160, 7722, 24950, 6, 375, 85639, 9318805, 9800058, 7, 756, 564041, 641631566, 98721672541, 16942485560, 8, 1372, 2663506, 17609835599, 69768979161580, 9463992096711104, 131898088386405, 9, 2304, 9976732

Offset: 1

Author

R. H. Hardin, Jun 30 2012

Keywords

• nonn
• tabl

Comments

Table starts

2, 3, 4, 5, 6;

12, 54, 160, 375, 756;

271, 7722, 85639, 564041, 2663506;

24950, 9318805, 641631566, 17609835599, 269462676001;

9800058, 98721672541, 69768979161580, 11798463876314995, 807203255071567008.

From Robert Israel, Jul 01 2020: (Start)

T(n,k) is the number of integer lattice points in kP where P is an (n^2)-dimensional polytope with vertices having integer coordinates. Therefore row n is an Ehrhart polynomial in k, with degree n^2 and rational coefficients. (End)

Examples

			Some solutions for n=3, k=1:
   0 0 1   0 0 0   0 0 0   0 1 0   0 0 0   1 0 0   1 0 0
   1 0 0   0 1 1   0 0 1   0 0 1   0 1 1   0 1 1   0 0 2
   0 0 1   0 0 1   1 2 0   0 0 0   0 1 1   0 0 2   0 0 0
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..41

Crossrefs

Row 2 is A019582(n+2). Rows 3 to 5: A214012, A214013, A214014.

Formula

Empirical: rows 1 2 3 are polynomials of degree 1 4 9.