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

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, 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, 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

Offset

1,3

Comments

Each row is an Ehrhart quasi-polynomial. - Robert Israel, May 04 2021

Links

R. H. Hardin, Table of n, a(n) for n = 1..291

Example

Some solutions for n=7 k=6
..3....2....3....3....5....2....3....4....0....6....3....5....1....6....0....1
..3....2....3....3....1....2....3....0....4....2....3....1....5....2....4....5
..6....1....3....4....0....0....2....1....3....4....5....3....5....5....2....1
..6....1....3....4....1....0....2....2....2....5....5....4....4....6....1....0
..3....2....3....3....3....2....3....2....2....4....3....3....3....4....2....3
..0....3....3....2....5....4....4....2....2....3....1....2....2....2....3....6
..0....3....3....2....6....4....4....3....1....4....1....3....1....3....2....5
..3....2....3....3....5....2....3....4....0....6....3....5....1....6....0....1
..3....2....3....3....1....2....3....0....4....2....3....1....5....2....4....5
Table starts
.1.1..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.....16....17
.2.3..4..7..10..13..16...21...26...31....36....43....50....57.....64....73
.2.3..6..9..14..25..36...47...64...87...110...143...176...209....258...311
.2.5..8.13..18..37..64...97..140..207...286...399...528...687....878..1127
.2.5..8.13..26..53.112..197..302..465...688..1013..1406..1995...2790..3759
.2.5..8.21..34..53.118..267..516..901..1454..2249..3264..5135...7616.11061
.2.7.16.31..52..83.228..515.1014.1903..3236..5351..8174.13719..21660.33377
.2.3..4.19..34.119.236..589.1236.2707..5062.10081.17712.30497..51072.83605
.2.3.10.37.104.261.574.1181.2560.5137.10922.23531.44970.81485.148250

Crossrefs

Row 3 is A008811(n+1).

Sequence in context: A023122 A375377 A375376 * A167286 A249821 A249822

Adjacent sequences: A200269 A200270 A200271 * A200273 A200274 A200275

Keyword

nonn,tabl

Author

R. H. Hardin Nov 15 2011

Status

approved