A183927 T(n,k)=Number of nondecreasing arrangements of n numbers in -k..k with sum zero and sum of squares not greater than n*k*(k+1)/3

1, 1, 1, 1, 2, 2, 1, 3, 4, 2, 1, 3, 5, 6, 2, 1, 4, 8, 12, 9, 3, 1, 4, 12, 23, 22, 13, 3, 1, 5, 17, 37, 48, 39, 17, 3, 1, 5, 22, 58, 93, 102, 63, 24, 4, 1, 6, 25, 83, 163, 220, 186, 104, 31, 4, 1, 7, 31, 112, 262, 434, 476, 332, 155, 38, 4, 1, 7, 38, 154, 414, 794, 1061, 979, 596, 226, 49

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...3...3....4.....4.....5.....5......6......7......7.......8.......8

.2..4...5...8...12....17....22....25.....31.....38.....45......53......62

.2..6..12..23...37....58....83...112....154....203....259.....329.....403

.2..9..22..48...93...163...262...414....618....877...1227....1661....2199

.3.13..39.102..220...434...794..1346...2190...3398...5106....7411...10494

.3.17..63.186..476..1061..2117..3998...7036..11808..19093...29687...44730

.3.24.104.332..979..2414..5278.10966..20984..37693..65732..109170..174209

.4.31.155.596.1888..5166.12584.28096..58118.113204.209399..370563..631264

.4.38.226.976.3493.10526.27893.67867.151415.315288.624895.1175933.2117218

Links

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

Example

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

Crossrefs

Sequence in context: A212306 A339708 A080242 * A035317 A368296 A103923

Adjacent sequences: A183924 A183925 A183926 * A183928 A183929 A183930

Keyword

nonn,tabl

Author

R. H. Hardin Jan 08 2011

Status

approved