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%I #8 Nov 11 2019 16:02:24
%S 1,1,2,1,3,2,1,4,3,2,1,5,6,3,2,1,6,9,8,7,2,1,7,12,17,14,9,2,1,8,17,26,
%T 27,18,9,2,1,9,22,43,58,37,24,15,2,1,10,27,64,111,108,85,56,7,2,1,11,
%U 34,89,182,245,202,169,26,3,2,1,12,41,122,279,454,429,394,151,26,11,2,1,13,48
%N T(n,k)=Number of 0..k arrays x(0..n) of n+1 elements with zero n-1st differences
%C Table starts
%C .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
%C .2..3..6...9..12...17....22....27....34.....41.....48.....57......66......75
%C .2..3..8..17..26...43....64....89...122....163....208....269.....334.....407
%C .2..7.14..27..58..111...182...279...404....617....872...1199....1580....2045
%C .2..9.18..37.108..245...454...759..1172...2001...3144...4663....6568....8945
%C .2..9.24..85.202..429..1046..2145..4022...6955..11438..17927...26868...41817
%C .2.15.56.169.394..855..2546..6179.12710..23899..41522..68427..106948..183797
%C .2..7.26.151.468.1863..5056.12965.29904..64603.124728.243309..432190..748301
%C .2..3.26.219.848.3573.11638.31507.84560.198435.418330.878657.1704398.3107463
%C T(n,k) is the number of integer lattice points in k*C(n) where C(n) is the polytope in R^(n+1) defined by two linear equations and the bounds 0 <= x_i <= 1. Since the vertices of this polytope have rational coordinates, T(n,k) for each fixed n is an Ehrhart quasi-polynomial of degree n-1. - _Robert Israel_, Nov 11 2019
%H R. H. Hardin, <a href="/A200082/b200082.txt">Table of n, a(n) for n = 1..268</a>
%e Some solutions for n=7 k=6
%e ..1....4....5....4....5....0....2....6....0....4....6....1....2....3....1....4
%e ..5....2....3....5....0....1....1....1....4....5....4....3....0....6....0....0
%e ..2....6....4....4....5....3....2....3....6....3....0....5....2....3....4....2
%e ..1....6....3....3....5....3....3....5....6....2....0....4....4....0....6....3
%e ..3....3....1....3....1....2....3....5....5....3....2....2....4....0....5....2
%e ..5....2....1....4....0....2....2....4....4....5....2....2....2....3....3....1
%e ..4....5....4....5....5....3....1....4....3....6....0....4....0....6....2....2
%e ..1....4....5....4....5....0....2....6....0....4....6....1....2....3....1....4
%Y Row 3 is A008810(n+1)
%K nonn,tabl
%O 1,3
%A _R. H. Hardin_ Nov 13 2011
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