A214592 Number of nXnXn triangular 0..5 arrays with every horizontal row having the same average value.

6, 18, 312, 33352, 20608352, 69920063852, 1279414854562952, 126404181535040391152, 67823930097039015417498752, 198754894778868023542228903871252, 3195893205534165606040279967148673282502, 283070945017969156158537463029538134823210477502

Offset: 1

Author

R. H. Hardin, Jul 22 2012

Keywords

• nonn
• changed

Examples

			Some solutions for n=4
.....2........3........1........2........2........2........2........2
....1.3......3.3......2.0......1.3......0.4......3.1......1.3......1.3
...2.4.0....3.1.5....2.1.0....1.5.0....4.2.0....0.2.4....3.1.2....1.4.1
..3.3.2.0..4.3.0.5..0.2.1.1..1.2.5.0..3.1.3.1..2.1.2.3..0.2.5.1..1.5.1.1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..52

Crossrefs

Column 5 of A214595.

Programs

PARI

apply( {A214592(n)=A214595(n,5)}, [1..12]) \\ M. F. Hasler, Aug 21 2025

Formula

From M. F. Hasler, Aug 21 2025: (Start)

a(n) == 2 (mod 10) for n > 2, (mod 50) for n > 3, (mod 2500) for n > 10, (mod 25000) for n > 21, (mod 125000000000) for n > 26.

a(n) = Sum_{k=0..5} Product_{L=2..n} NC(k*L, L, 5), where NC(s, n, m) is the number of compositions with sum s and n parts between 0 and m. (End)