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

1,1

Comments

Row 5 of A200942.

Links

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

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

Example

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

Crossrefs

Cf. A200942.

Sequence in context: A062981 A069622 A334193 * A137189 A028503 A100291

Adjacent sequences: A200941 A200942 A200943 * A200945 A200946 A200947

Keyword

nonn

Author

R. H. Hardin Nov 24 2011

Status

approved