A200765 Number of 0..n arrays x(0..4) of 5 elements with nondecreasing average value.
6, 32, 110, 297, 679, 1387, 2583, 4500, 7410, 11669, 17687, 25980, 37111, 51787, 70763, 94950, 125323, 163042, 209312, 265570, 333296, 414214, 510106, 623032, 755080, 908676, 1086266, 1290643, 1524638, 1791469, 2094349, 2436949, 2822922
Offset: 1
Keywords
Examples
Some solutions for n=8 ..1....0....0....2....0....1....1....0....0....0....0....2....2....5....0....1 ..5....2....0....2....0....1....1....4....1....3....8....4....3....7....2....6 ..7....1....2....2....6....1....3....5....4....4....8....6....7....7....8....7 ..5....3....8....3....3....8....3....5....3....4....8....8....4....8....7....5 ..8....7....3....3....8....4....8....8....8....8....6....8....4....7....5....5
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Formula
Empirical: a(n) = a(n-1) +2*a(n-2) -3*a(n-4) -3*a(n-5) +3*a(n-6) +3*a(n-7) +a(n-8) -3*a(n-9) -3*a(n-10) +a(n-11) +3*a(n-12) +3*a(n-13) -3*a(n-14) -3*a(n-15) +2*a(n-17) +a(n-18) -a(n-19)
Empirical g.f.: -x*(-6 -26*x -66*x^2 -123*x^3 -180*x^4 -228*x^5 -246*x^6 -250*x^7 -240*x^8 -222*x^9 -184*x^10 -129*x^11 -69*x^12 -21*x^13 -2*x^14 -x^15 -2*x^16 -x^17+x^18) / ( (x^2+1) *(x^4+1) *(1+x+x^2)^2 *(1+x)^3 *(x-1)^6 ). - R. J. Mathar, Nov 22 2011
Comments