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A214592
Number of nXnXn triangular 0..5 arrays with every horizontal row having the same average value.
2
6, 18, 312, 33352, 20608352, 69920063852, 1279414854562952, 126404181535040391152, 67823930097039015417498752, 198754894778868023542228903871252, 3195893205534165606040279967148673282502, 283070945017969156158537463029538134823210477502
OFFSET
1,1
LINKS
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)
EXAMPLE
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
PROG
(PARI) apply( {A214592(n)=A214595(n, 5)}, [1..12]) \\ M. F. Hasler, Aug 21 2025
CROSSREFS
Column 5 of A214595.
Sequence in context: A052139 A354019 A052682 * A372522 A130437 A119813
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 22 2012
STATUS
approved