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 A200082 T(n,k)=Number of 0..k arrays x(0..n) of n+1 elements with zero n-1st differences 11
 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, 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, 34, 89, 182, 245, 202, 169, 26, 3, 2, 1, 12, 41, 122, 279, 454, 429, 394, 151, 26, 11, 2, 1, 13, 48 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Table starts .1..1..1...1...1....1.....1.....1.....1......1......1......1.......1.......1 .2..3..4...5...6....7.....8.....9....10.....11.....12.....13......14......15 .2..3..6...9..12...17....22....27....34.....41.....48.....57......66......75 .2..3..8..17..26...43....64....89...122....163....208....269.....334.....407 .2..7.14..27..58..111...182...279...404....617....872...1199....1580....2045 .2..9.18..37.108..245...454...759..1172...2001...3144...4663....6568....8945 .2..9.24..85.202..429..1046..2145..4022...6955..11438..17927...26868...41817 .2.15.56.169.394..855..2546..6179.12710..23899..41522..68427..106948..183797 .2..7.26.151.468.1863..5056.12965.29904..64603.124728.243309..432190..748301 .2..3.26.219.848.3573.11638.31507.84560.198435.418330.878657.1704398.3107463 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 LINKS R. H. Hardin, Table of n, a(n) for n = 1..268 EXAMPLE Some solutions for n=7 k=6 ..1....4....5....4....5....0....2....6....0....4....6....1....2....3....1....4 ..5....2....3....5....0....1....1....1....4....5....4....3....0....6....0....0 ..2....6....4....4....5....3....2....3....6....3....0....5....2....3....4....2 ..1....6....3....3....5....3....3....5....6....2....0....4....4....0....6....3 ..3....3....1....3....1....2....3....5....5....3....2....2....4....0....5....2 ..5....2....1....4....0....2....2....4....4....5....2....2....2....3....3....1 ..4....5....4....5....5....3....1....4....3....6....0....4....0....6....2....2 ..1....4....5....4....5....0....2....6....0....4....6....1....2....3....1....4 CROSSREFS Row 3 is A008810(n+1) Sequence in context: A167286 A249821 A249822 * A052310 A052313 A271355 Adjacent sequences: A200079 A200080 A200081 * A200083 A200084 A200085 KEYWORD nonn,tabl AUTHOR R. H. Hardin Nov 13 2011 STATUS approved

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Last modified October 3 11:38 EDT 2023. Contains 365861 sequences. (Running on oeis4.)