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A200085 Number of 0..n arrays x(0..6) of 7 elements with zero 5th differences.

%I A200085 #7 Jul 22 2025 15:40:58
%S A200085 2,9,18,37,108,245,454,759,1172,2001,3144,4663,6568,8945,12690,17353,
%T A200085 23022,29787,37710,48921,62130,77465,95100,115177,141596,171767,
%U A200085 205850,244065,286652,340277,400038,466375,539488,619685,717388,824733,942014
%N A200085 Number of 0..n arrays x(0..6) of 7 elements with zero 5th differences.
%C A200085 Row 6 of A200082
%H A200085 R. H. Hardin, <a href="/A200085/b200085.txt">Table of n, a(n) for n = 1..200</a>
%F A200085 Empirical: a(n) = a(n-1) +a(n-5) -a(n-7) +a(n-10) -2*a(n-11) +a(n-12) -a(n-16) +a(n-17) -a(n-20) +a(n-21) -a(n-25) +2*a(n-26) -a(n-27) +a(n-30) -a(n-32) -a(n-36) +a(n-37) +a(n-45) -a(n-46) -a(n-50) +a(n-52) -a(n-55) +2*a(n-56) -a(n-57) +a(n-61) -a(n-62) +a(n-65) -a(n-66) +a(n-70) -2*a(n-71) +a(n-72) -a(n-75) +a(n-77) +a(n-81) -a(n-82)
%e A200085 Some solutions for n=6
%e A200085 ..6....3....0....6....5....5....5....6....5....0....2....5....0....3....0....0
%e A200085 ..5....5....1....4....1....6....5....2....1....4....1....2....3....3....5....6
%e A200085 ..3....3....0....3....1....2....6....0....3....6....2....3....1....5....5....6
%e A200085 ..3....1....0....2....3....0....5....1....4....5....3....5....0....6....3....5
%e A200085 ..5....1....2....1....5....2....2....4....2....2....3....6....2....5....1....5
%e A200085 ..6....3....5....1....5....5....0....6....0....0....2....5....5....3....0....5
%e A200085 ..0....5....6....4....1....1....5....2....6....4....1....2....3....3....0....1
%K A200085 nonn
%O A200085 1,1
%A A200085 _R. H. Hardin_ Nov 13 2011