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%I #4 Feb 01 2016 10:24:16
%S 2,4,11,33,114,435,1828,8347,40967,213476,1167038,6620563,38616800,
%T 229908144,1389394409,8488437842,52275301038,323844494931,
%U 2015202856151,12583558074610,78792289312786,494476637793884,3109144620092506
%N Number of length-(n+1) 0..6 arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.
%C Column 6 of A268327.
%H R. H. Hardin, <a href="/A268325/b268325.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 85*a(n-1) -3366*a(n-2) +82295*a(n-3) -1386925*a(n-4) +17019210*a(n-5) -156331765*a(n-6) +1084941555*a(n-7) -5636724036*a(n-8) +21085378015*a(n-9) -50325001951*a(n-10) +37617575820*a(n-11) +213182974620*a(n-12) -813092997160*a(n-13) +770630574930*a(n-14) +2257030578230*a(n-15) -6653453677281*a(n-16) +247414659915*a(n-17) +21051181958044*a(n-18) -16718457793465*a(n-19) -43997340297789*a(n-20) +53879923261450*a(n-21) +76684670354671*a(n-22) -100035381928785*a(n-23) -126944916371090*a(n-24) +114738194825025*a(n-25) +187188954935145*a(n-26) -51075152814970*a(n-27) -196841758256594*a(n-28) -63278370502380*a(n-29) +98176306220916*a(n-30) +99869982678040*a(n-31) +19690930153560*a(n-32) -26581558465280*a(n-33) -25769657503680*a(n-34) -11894859049920*a(n-35) -3433657832064*a(n-36) -649913978880*a(n-37) -78779602944*a(n-38) -5563468800*a(n-39) -174182400*a(n-40)
%e Some solutions for n=9
%e ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e ..1....1....1....1....1....1....1....1....1....1....0....1....0....1....0....1
%e ..2....2....2....2....2....0....0....2....0....2....1....2....1....2....1....2
%e ..0....3....3....3....3....2....0....3....0....0....2....3....0....3....1....1
%e ..3....2....4....4....2....3....0....4....2....2....3....4....2....1....0....0
%e ..4....4....2....0....0....4....2....0....0....3....4....3....3....2....1....3
%e ..3....0....5....3....0....5....3....4....0....0....3....2....0....0....2....4
%e ..0....0....3....2....3....3....0....2....1....3....5....1....2....4....1....3
%e ..1....5....4....5....1....0....2....0....3....1....0....2....3....1....1....4
%e ..4....3....5....1....3....1....0....0....0....4....1....1....4....0....2....1
%Y Cf. A268327.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 01 2016
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