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A200945 Number of 0..n arrays x(0..5) of 6 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.

%I A200945 #7 Jul 22 2025 16:01:45
%S A200945 1,6,40,61,20,134,536,1613,4023,8842,17681,32835,57465,95825,153352,
%T A200945 237104,355792,520226,743448,1041280,1432241,1938480,2585494,3403125,
%U A200945 4425342,5691528,7245651,9138376,11425775,14171497,17445655,21327385
%N A200945 Number of 0..n arrays x(0..5) of 6 elements with nondecreasing average value and 0..n occur with instance counts within one of each other.
%C A200945 Row 6 of A200942
%H A200945 R. H. Hardin, <a href="/A200945/b200945.txt">Table of n, a(n) for n = 1..143</a>
%F A200945 Empirical: a(n) = -a(n-1) -a(n-2) +a(n-6) +2*a(n-7) +4*a(n-8) +3*a(n-9) +3*a(n-10) +2*a(n-11) +2*a(n-12) -3*a(n-14) -4*a(n-15) -5*a(n-16) -5*a(n-17) -7*a(n-18) -7*a(n-19) -5*a(n-20) -2*a(n-21) +3*a(n-24) +6*a(n-25) +8*a(n-26) +7*a(n-27) +6*a(n-28) +7*a(n-29) +7*a(n-30) +5*a(n-31) +a(n-32) -a(n-35) -5*a(n-36) -7*a(n-37) -7*a(n-38) -6*a(n-39) -7*a(n-40) -8*a(n-41) -6*a(n-42) -3*a(n-43) +2*a(n-46) +5*a(n-47) +7*a(n-48) +7*a(n-49) +5*a(n-50) +5*a(n-51) +4*a(n-52) +3*a(n-53) -2*a(n-55) -2*a(n-56) -3*a(n-57) -3*a(n-58) -4*a(n-59) -2*a(n-60) -a(n-61) +a(n-65) +a(n-66) +a(n-67) for n>71
%e A200945 Some solutions for n=8
%e A200945 ..2....0....0....0....0....0....0....0....0....0....0....0....0....0....1....1
%e A200945 ..3....1....2....2....2....2....2....1....1....2....5....1....2....4....2....4
%e A200945 ..4....4....1....1....3....7....6....7....7....1....6....4....1....2....3....8
%e A200945 ..5....3....4....7....5....3....3....4....5....8....4....2....4....6....5....5
%e A200945 ..8....7....5....4....6....6....4....3....8....5....8....8....6....5....6....7
%e A200945 ..7....8....8....8....8....4....5....8....6....6....7....5....8....8....8....6
%K A200945 nonn
%O A200945 1,2
%A A200945 _R. H. Hardin_ Nov 24 2011