A214596 Number of 3X3X3 triangular 0..n arrays with every horizontal row having the same average value.

2, 23, 62, 157, 312, 601, 986, 1619, 2426, 3589, 5028, 6997, 9314, 12371, 15914, 20377, 25488, 31789, 38846, 47399, 56906, 68161, 80592, 95137, 111002, 129383, 149342, 172141, 196800, 224761, 254762, 288563, 324722, 365077, 408132, 455941, 506666

Offset: 1

Author

R. H. Hardin, Jul 22 2012

Keywords

• nonn
• changed

Examples

			Some solutions for n=4
....3......2......1......1......2......2......3......2......3......2......2
...2.4....1.3....1.1....2.0....3.1....0.4....3.3....1.3....4.2....4.0....0.4
..2.4.3..3.2.1..1.0.2..1.1.1..3.1.2..2.0.4..3.2.4..3.3.0..2.3.4..1.2.3..0.3.3
		

Links

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

Crossrefs

Row 3 of A214595.

Formula

Empirical: a(n) = 3*a(n-2) +2*a(n-3) -3*a(n-4) -6*a(n-5) +6*a(n-7) +3*a(n-8) -2*a(n-9) -3*a(n-10) +a(n-12).

Empirical: G.f. ( -x*(2+23*x+56*x^2+84*x^3+86*x^4+87*x^5+60*x^6+23*x^7-2*x^9+x^11) ) / ( (1+x+x^2)^2*(1+x)^3*(x-1)^5 ). - R. J. Mathar, Jul 23 2012