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%I #5 Mar 31 2012 12:36:40
%S 5,15,42,113,297,767,1957,4947,12419,31006,77067,190855,471214,
%T 1160452,2851731,6995305,17133294,41909286,102399361,249960246,
%U 609662706,1485944622,3619527395,8811972483,21443566290,52161461882,126839318918
%N Number of 0..4 arrays x(0..n-1) of n elements with nondecreasing average value
%C Column 4 of A200763
%H R. H. Hardin, <a href="/A200760/b200760.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 18*a(n-1) -147*a(n-2) +718*a(n-3) -2324*a(n-4) +5207*a(n-5) -8163*a(n-6) +8783*a(n-7) -5967*a(n-8) +1216*a(n-9) +4359*a(n-10) -12032*a(n-11) +21061*a(n-12) -25355*a(n-13) +19242*a(n-14) -4565*a(n-15) -10182*a(n-16) +15832*a(n-17) -9350*a(n-18) -2623*a(n-19) +9836*a(n-20) -8451*a(n-21) +2304*a(n-22) +2965*a(n-23) -4284*a(n-24) +2384*a(n-25) -124*a(n-26) -752*a(n-27) +543*a(n-28) -103*a(n-29) -133*a(n-30) +128*a(n-31) -53*a(n-32) +19*a(n-33) -12*a(n-34) +3*a(n-35) +9*a(n-36) -6*a(n-37) -a(n-38) +2*a(n-39) -a(n-41)
%e Some solutions for n=8
%e ..0....0....0....0....0....0....0....0....1....0....1....0....1....1....0....0
%e ..0....1....0....2....2....1....0....1....1....2....1....0....1....1....4....0
%e ..0....2....0....1....2....1....3....2....4....1....1....0....2....2....4....4
%e ..2....2....1....2....3....1....1....1....3....1....4....4....4....3....3....2
%e ..2....2....3....4....2....2....3....2....3....1....2....4....2....3....3....3
%e ..3....3....2....2....4....2....3....4....3....2....4....2....2....4....3....2
%e ..2....2....4....3....3....4....3....3....4....2....4....2....2....3....3....3
%e ..4....2....4....2....4....2....2....4....4....2....3....4....4....3....3....3
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 22 2011