A200944 Number of 0..n arrays x(0..4) of 5 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.
2, 9, 17, 8, 44, 151, 398, 890, 1774, 3246, 5555, 9016, 14012, 21005, 30529, 43228, 59824, 81159, 108166, 141927, 183608, 234553, 296197, 370168, 458195, 562234, 684319, 826757, 991940, 1182536, 1401309, 1651348, 1935801, 2258191, 2622105
Offset: 1
Keywords
Examples
Some solutions for n=8 ..0....0....0....0....0....1....0....1....0....1....0....0....0....0....1....2 ..2....2....1....1....2....2....2....2....2....2....4....4....5....1....2....4 ..7....7....3....8....1....8....3....5....1....5....2....5....3....3....5....5 ..3....4....2....5....6....4....4....4....4....7....7....3....6....4....6....6 ..4....5....6....7....8....7....5....3....7....8....5....8....4....2....8....7
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A200942.
Formula
Empirical: a(n) = 2*a(n-2) +2*a(n-3) -a(n-4) -3*a(n-5) -a(n-6) +a(n-8) +a(n-9) +a(n-10) -a(n-11) -a(n-12) +a(n-13) +a(n-14) +a(n-15) -a(n-17) -3*a(n-18) -a(n-19) +2*a(n-20) +2*a(n-21) -a(n-23) for n>26.
Empirical g.f.: 2*x +9*x^2 +17*x^3 +x^4*(8+44*x +135*x^2+294*x^3 +508*x^4+744*x^5 +961*x^6+1122*x^7 +1203*x^8+1200*x^9 +1118*x^10+955*x^11 +734*x^12+496*x^13 +289*x^14+128*x^15 +35*x^16+x^17) / ( (x^2+1)*(x^4+x^3+x^2+x+1)*(x^4+1)*(1+x+x^2)^2*(1+x)^3*(x-1)^6 ). - R. J. Mathar, Nov 25 2011
Comments