A195805 T(n,k)=Number of triangular nXnXn 0..k arrays with all rows and diagonals having the same length having the same sum, with corners zero.

1, 1, 1, 1, 1, 2, 1, 1, 3, 8, 1, 1, 4, 27, 16, 1, 1, 5, 64, 105, 64, 1, 1, 6, 125, 496, 1695, 1184, 1, 1, 7, 216, 1759, 24928, 284427, 5300, 1, 1, 8, 343, 5052, 213319, 17528896, 11606931, 130324, 1, 1, 9, 512, 12469, 1274808

Offset: 1

Author

R. H. Hardin Sep 23 2011

Keywords

• nonn
• tabl

Comments

Table starts

....1........1........1......1.......1.....1...1.1.1.1

....1........1........1......1.......1.....1...1.1.1

....2........3........4......5.......6.....7...8.9

....8.......27.......64....125.....216...343.512

...16......105......496...1759....5052.12469

...64.....1695....24928.213319.1274808

.1184...284427.17528896

.5300.11606931

Examples

			Some solutions for n=4 k=4
.....0........0........0........0........0........0........0........0
....3.1......3.4......2.4......0.3......3.2......3.0......1.4......1.2
...1.3.3....4.4.3....4.2.2....3.2.0....2.4.3....0.3.3....4.2.1....2.3.1
..0.3.1.0..0.3.4.0..0.2.4.0..0.0.3.0..0.3.2.0..0.3.0.0..0.1.4.0..0.1.2.0