A214908 Number of 4X4X4 triangular 0..n arrays with every horizontal row nondecreasing and having the same average value

2, 14, 50, 182, 458, 1184, 2490, 5213, 9722, 17864, 30284, 51088, 80840, 127040, 191162, 285357, 410940, 589294, 820180, 1136378, 1538406, 2072864, 2738172, 3606249, 4667108, 6021672, 7659902, 9714004, 12163526, 15197912, 18774496

Offset

1,1

Comments

Row 4 of A214906

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = a(n-4) +2*a(n-6) +2*a(n-8) +2*a(n-9) -2*a(n-10) -2*a(n-12) -2*a(n-13) -4*a(n-14) -4*a(n-15) -a(n-16) -4*a(n-17) +a(n-18) +4*a(n-19) +a(n-20) +4*a(n-21) +5*a(n-22) +8*a(n-23) +3*a(n-24) +2*a(n-25) +4*a(n-26) -4*a(n-27) -3*a(n-28) -2*a(n-29) -6*a(n-30) -8*a(n-31) -6*a(n-32) -2*a(n-33) -3*a(n-34) -4*a(n-35) +4*a(n-36) +2*a(n-37) +3*a(n-38) +8*a(n-39) +5*a(n-40) +4*a(n-41) +a(n-42) +4*a(n-43) +a(n-44) -4*a(n-45) -a(n-46) -4*a(n-47) -4*a(n-48) -2*a(n-49) -2*a(n-50) -2*a(n-52) +2*a(n-53) +2*a(n-54) +2*a(n-56) +a(n-58) -a(n-62)

Example

Some solutions for n=4
.....2........2........2........2........3........2........2........2
....2.2......1.3......1.3......2.2......2.4......1.3......1.3......0.4
...1.1.4....1.2.3....0.3.3....2.2.2....2.3.4....1.2.3....0.3.3....0.2.4
..1.1.3.3..1.1.3.3..0.1.3.4..0.1.3.4..1.3.4.4..0.2.2.4..2.2.2.2..1.2.2.3

Crossrefs

Sequence in context: A241232 A163796 A153978 * A143553 A341493 A064363

Adjacent sequences: A214905 A214906 A214907 * A214909 A214910 A214911

Keyword

nonn

Author

R. H. Hardin Jul 29 2012

Status

approved