cp's OEIS Frontend

A200272 T(n,k) is the number of 0..k arrays x(0..n+1) of n+2 elements with zero n-1st differences.

%I A200272 #15 Jul 22 2025 15:46:15
%S A200272 1,1,2,1,3,2,1,4,3,2,1,5,4,3,2,1,6,7,6,5,2,1,7,10,9,8,5,2,1,8,13,14,
%T A200272 13,8,5,2,1,9,16,25,18,13,8,7,2,1,10,21,36,37,26,21,16,3,2,1,11,26,47,
%U A200272 64,53,34,31,4,3,2,1,12,31,64,97,112,53,52,19,10,7,2,1,13,36,87,140,197,118,83
%N A200272 T(n,k) is the number of 0..k arrays x(0..n+1) of n+2 elements with zero n-1st differences.
%C A200272 Each row is an Ehrhart quasi-polynomial. - _Robert Israel_, May 04 2021
%H A200272 R. H. Hardin, <a href="/A200272/b200272.txt">Table of n, a(n) for n = 1..291</a>
%e A200272 Some solutions for n=7 k=6
%e A200272 ..3....2....3....3....5....2....3....4....0....6....3....5....1....6....0....1
%e A200272 ..3....2....3....3....1....2....3....0....4....2....3....1....5....2....4....5
%e A200272 ..6....1....3....4....0....0....2....1....3....4....5....3....5....5....2....1
%e A200272 ..6....1....3....4....1....0....2....2....2....5....5....4....4....6....1....0
%e A200272 ..3....2....3....3....3....2....3....2....2....4....3....3....3....4....2....3
%e A200272 ..0....3....3....2....5....4....4....2....2....3....1....2....2....2....3....6
%e A200272 ..0....3....3....2....6....4....4....3....1....4....1....3....1....3....2....5
%e A200272 ..3....2....3....3....5....2....3....4....0....6....3....5....1....6....0....1
%e A200272 ..3....2....3....3....1....2....3....0....4....2....3....1....5....2....4....5
%e A200272 Table starts
%e A200272 .1.1..1..1...1...1...1....1....1....1.....1.....1.....1.....1......1.....1
%e A200272 .2.3..4..5...6...7...8....9...10...11....12....13....14....15.....16....17
%e A200272 .2.3..4..7..10..13..16...21...26...31....36....43....50....57.....64....73
%e A200272 .2.3..6..9..14..25..36...47...64...87...110...143...176...209....258...311
%e A200272 .2.5..8.13..18..37..64...97..140..207...286...399...528...687....878..1127
%e A200272 .2.5..8.13..26..53.112..197..302..465...688..1013..1406..1995...2790..3759
%e A200272 .2.5..8.21..34..53.118..267..516..901..1454..2249..3264..5135...7616.11061
%e A200272 .2.7.16.31..52..83.228..515.1014.1903..3236..5351..8174.13719..21660.33377
%e A200272 .2.3..4.19..34.119.236..589.1236.2707..5062.10081.17712.30497..51072.83605
%e A200272 .2.3.10.37.104.261.574.1181.2560.5137.10922.23531.44970.81485.148250
%Y A200272 Row 3 is A008811(n+1).
%K A200272 nonn,tabl
%O A200272 1,3
%A A200272 _R. H. Hardin_ Nov 15 2011