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A268327 T(n,k)=Number of length-(n+1) 0..k arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.

%I A268327 #4 Feb 01 2016 10:26:15
%S A268327 2,2,3,2,4,6,2,4,10,11,2,4,11,25,22,2,4,11,32,66,43,2,4,11,33,102,177,
%T A268327 86,2,4,11,33,113,337,485,171,2,4,11,33,114,418,1148,1348,342,2,4,11,
%U A268327 33,114,434,1644,3984,3797,683,2,4,11,33,114,435,1806,6729,14030,10812,1366,2,4
%N A268327 T(n,k)=Number of length-(n+1) 0..k arrays with new values introduced in sequential order, and with new repeated values introduced in sequential order, both starting with zero.
%C A268327 Table starts
%C A268327 ...2.....2.....2......2......2......2......2......2......2......2......2......2
%C A268327 ...3.....4.....4......4......4......4......4......4......4......4......4......4
%C A268327 ...6....10....11.....11.....11.....11.....11.....11.....11.....11.....11.....11
%C A268327 ..11....25....32.....33.....33.....33.....33.....33.....33.....33.....33.....33
%C A268327 ..22....66...102....113....114....114....114....114....114....114....114....114
%C A268327 ..43...177...337....418....434....435....435....435....435....435....435....435
%C A268327 ..86...485..1148...1644...1806...1828...1829...1829...1829...1829...1829...1829
%C A268327 .171..1348..3984...6729...8052...8347...8376...8377...8377...8377...8377...8377
%C A268327 .342..3797.14030..28306..37851..40967..41466..41503..41504..41504..41504..41504
%C A268327 .683.10812.49973.121290.184910.213476.220115.220911.220957.220958.220958.220958
%H A268327 R. H. Hardin, <a href="/A268327/b268327.txt">Table of n, a(n) for n = 1..9999</a>
%F A268327 Empirical for column k:
%F A268327 k=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3)
%F A268327 k=2: a(n) = 7*a(n-1) -14*a(n-2) +21*a(n-4) -7*a(n-5) -6*a(n-6)
%F A268327 k=3: [order 12]
%F A268327 k=4: [order 19]
%F A268327 k=5: [order 29]
%F A268327 k=6: [order 40]
%F A268327 k=7: [order 54]
%e A268327 Some solutions for n=9 k=4
%e A268327 ..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
%e A268327 ..1....0....1....1....0....1....1....1....0....1....0....1....1....1....1....0
%e A268327 ..2....1....0....2....0....2....2....2....1....2....0....2....2....2....2....1
%e A268327 ..0....1....0....0....0....0....3....1....1....3....1....3....3....0....0....1
%e A268327 ..2....2....2....0....1....2....0....2....2....1....0....0....1....3....3....2
%e A268327 ..0....2....0....1....2....3....1....3....3....3....2....4....2....2....0....2
%e A268327 ..1....3....3....3....3....1....0....0....4....2....1....3....4....0....0....0
%e A268327 ..0....1....0....1....1....0....0....1....1....0....0....1....2....2....0....3
%e A268327 ..1....1....1....0....2....1....0....3....4....1....1....4....3....4....1....1
%e A268327 ..2....0....2....3....3....2....2....4....3....2....1....2....0....2....0....4
%Y A268327 Column 1 is A005578(n+1).
%K A268327 nonn,tabl
%O A268327 1,1
%A A268327 _R. H. Hardin_, Feb 01 2016