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A200158 Number of 0..n arrays x(0..6) of 7 elements with zero 6th difference.

%I A200158 #7 Jul 22 2025 15:42:19
%S A200158 2,45,182,685,2036,5153,11370,23035,43284,76523,129052,208597,324900,
%T A200158 491519,723994,1041095,1467042,2029069,2759166,3697749,4888510,
%U A200158 6381185,8237500,10523625,13313648,16697587,20769202,25633157,31415424,38246327
%N A200158 Number of 0..n arrays x(0..6) of 7 elements with zero 6th difference.
%C A200158 Row 7 of A200154
%H A200158 R. H. Hardin, <a href="/A200158/b200158.txt">Table of n, a(n) for n = 1..200</a>
%F A200158 Empirical: a(n) = 2*a(n-1) -a(n-2) +2*a(n-6) -4*a(n-7) +2*a(n-8) -a(n-12) +2*a(n-13) -a(n-14) +2*a(n-15) -4*a(n-16) +2*a(n-17) +a(n-20) -6*a(n-21) +9*a(n-22) -4*a(n-23) -2*a(n-26) +6*a(n-27) -6*a(n-28) +2*a(n-29) -a(n-30) +2*a(n-31) -2*a(n-33) +a(n-34) -2*a(n-35) +6*a(n-36) -6*a(n-37) +2*a(n-38) +4*a(n-41) -9*a(n-42) +6*a(n-43) -a(n-44) -2*a(n-47) +4*a(n-48) -2*a(n-49) +a(n-50) -2*a(n-51) +a(n-52) -2*a(n-56) +4*a(n-57) -2*a(n-58) +a(n-62) -2*a(n-63) +a(n-64)
%e A200158 Some solutions for n=6
%e A200158 ..1....3....1....4....0....2....1....5....0....2....2....1....5....5....2....0
%e A200158 ..6....0....1....6....6....5....5....6....3....1....0....6....3....0....0....6
%e A200158 ..5....1....6....3....3....3....0....0....2....0....3....6....0....3....2....2
%e A200158 ..2....1....5....4....1....2....0....1....2....2....1....3....3....5....1....1
%e A200158 ..0....1....1....6....2....3....2....4....2....3....0....2....5....4....1....4
%e A200158 ..1....3....0....4....4....4....1....2....1....1....5....5....1....2....5....6
%e A200158 ..6....5....0....1....5....2....5....3....4....5....3....5....4....2....3....2
%K A200158 nonn
%O A200158 1,1
%A A200158 _R. H. Hardin_ Nov 13 2011