A214541 Number of 3X3X3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and every horizontal row having the same average value.
2, 15, 38, 79, 152, 263, 418, 643, 942, 1329, 1832, 2463, 3234, 4185, 5326, 6677, 8280, 10153, 12314, 14817, 17678, 20923, 24608, 28757, 33394, 38587, 44358, 50739, 57800, 65571, 74082, 83415, 93598, 104669, 116712, 129763, 143858, 159093, 175502
Offset: 1
Keywords
Examples
Some solutions for n=4 ....3......2......3......2......3......3......1......0......2......2......1 ...2.4....3.1....4.2....3.1....3.3....3.3....1.1....0.0....3.1....2.2....0.2 ..4.1.4..3.3.0..4.1.4..2.4.0..3.2.4..3.3.3..1.1.1..0.0.0..3.1.2..1.3.2..0.1.2
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = 2*a(n-1) -3*a(n-4) +3*a(n-6) -2*a(n-9) +a(n-10).
Empirical: G.f. -x*(2+11*x+8*x^2+3*x^3+4*x^5-x^7-2*x^8+x^9) / ( (1+x)*(1+x+x^2)^2*(x-1)^5 ). - R. J. Mathar, Jul 23 2012
Comments