A183935 T(n,k)=Number of nondecreasing arrangements of n numbers in -k..k with sum zero and sum of squares less than n*k*(k+1)/3

1, 1, 1, 1, 2, 1, 1, 2, 2, 2, 1, 3, 5, 5, 2, 1, 4, 8, 11, 8, 2, 1, 4, 12, 23, 21, 10, 3, 1, 5, 15, 36, 48, 36, 15, 3, 1, 5, 20, 56, 89, 97, 60, 21, 3, 1, 6, 24, 83, 157, 211, 186, 95, 26, 4, 1, 7, 31, 110, 262, 421, 457, 332, 143, 35, 4, 1, 7, 38, 152, 408, 777, 1030, 938, 571, 212, 44, 4, 1

Offset

1,5

Comments

k*(k+1)/3 is the average squared value over -k..k

Table starts

.1..1...1...1....1.....1.....1.....1......1......1......1.......1.......1

.1..2...2...3....4.....4.....5.....5......6......7......7.......8.......8

.1..2...5...8...12....15....20....24.....31.....38.....45......53......58

.2..5..11..23...36....56....83...110....152....203....257.....328.....403

.2..8..21..48...89...157...262...408....610....877...1217....1653....2199

.2.10..36..97..211...421...777..1324...2155...3365...5048....7347...10411

.3.15..60.186..457..1030..2117..3931...6955..11808..18890...29443...44730

.3.21..95.332..938..2349..5278.10781..20679..37693..65031..108168..174209

.3.26.143.571.1828..5033.12353.27652..57369.112098.207557..367766..627381

.4.35.212.976.3390.10278.27893.66846.149679.315288.619458.1167215.2117218

Links

R. H. Hardin, Table of n, a(n) for n = 1..642

Example

Some solutions for n=5
.-3...-2...-2...-3...-1...-3...-3...-4...-2...-4...-4...-2...-4...-3...-2...-1
.-2...-1...-2...-1...-1...-1...-3....0...-1...-2....0...-1....1...-1...-1...-1
.-1....1....0...-1...-1....0....2....1...-1....2....0...-1....1....0....0....0
..3....1....2....1...-1....0....2....1....0....2....0....1....1....1....1....0
..3....1....2....4....4....4....2....2....4....2....4....3....1....3....2....2

Crossrefs

Sequence in context: A131335 A225332 A209032 * A046081 A366417 A190592

Adjacent sequences: A183932 A183933 A183934 * A183936 A183937 A183938

Keyword

nonn,tabl

Author

R. H. Hardin Jan 08 2011

Status

approved