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%I #6 Mar 31 2012 12:36:39
%S 1,1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,6,5,4,3,2,1,7,6,5,4,3,2,1,8,9,6,5,4,
%T 3,2,1,9,12,9,6,5,4,3,2,1,10,15,14,9,6,5,4,3,2,1,11,18,19,12,7,6,5,4,
%U 3,2,1,12,21,24,17,12,7,6,5,4,3,2,1,13,24,33,22,19,8,7,6,7,4,3,2,1,14,29,42,37
%N T(n,k)=Number of 0..k arrays x(0..n+3) of n+4 elements with zero n-1st differences
%C Table starts
%C .1.1.1.1..1..1..1..1..1..1..1...1...1...1...1...1...1...1...1...1..1..1.1
%C .2.3.4.5..6..7..8..9.10.11.12..13..14..15..16..17..18..19..20..21.22.23
%C .2.3.4.5..6..9.12.15.18.21.24..29..34..39..44..49..54..61..68..75.82
%C .2.3.4.5..6..9.14.19.24.33.42..53..64..77..94.115.136.159.182.209
%C .2.3.4.5..6..9.12.17.22.37.52..71..94.117.148.197.250.305.364
%C .2.3.4.5..6..7.12.19.28.43.66..97.132.177.242.321.420.529
%C .2.3.4.5..6..7..8.17.26.41.60..93.130.187.256.373.522
%C .2.3.4.5..6..7.10.23.42.63.88.117.158.241.356.525
%C .2.3.4.5..6..9.12.21.34.51.72.123.190.311.452
%C .2.3.4.7.10.13.16.23.34.49.72.123.208.367
%H R. H. Hardin, <a href="/A200443/b200443.txt">Table of n, a(n) for n = 1..268</a>
%e Some.solutions.for.n=8.k=8..
%e ..8....4....2....0....6....1....0....8....7....0....8....8....5....1....1....8
%e ..8....1....2....6....6....8....0....6....7....8....2....1....5....0....1....0
%e ..8....7....2....6....6....4....0....2....7....6....2....5....5....4....1....2
%e ..8....8....2....6....6....1....0....0....7....2....2....8....5....7....1....6
%e ..8....4....2....7....6....1....0....1....7....0....1....8....5....8....1....8
%e ..8....0....2....8....6....2....0....4....7....1....0....7....5....8....1....7
%e ..8....0....2....8....6....2....0....7....7....4....0....7....5....8....1....4
%e ..8....4....2....7....6....1....0....8....7....7....1....8....5....8....1....1
%e ..8....8....2....6....6....1....0....6....7....8....2....8....5....7....1....0
%e ..8....7....2....6....6....4....0....2....7....6....2....5....5....4....1....2
%e ..8....1....2....6....6....8....0....0....7....2....2....1....5....0....1....6
%e ..8....4....2....0....6....1....0....8....7....0....8....8....5....1....1....8
%Y Row 3 is A008813
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Nov 18 2011
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