A188181 - OEIS

A188181

T(n,k) is the number of strictly increasing arrangements of n numbers in -(n+k-2)..(n+k-2) with sum zero.

1, 1, 1, 1, 2, 2, 1, 3, 5, 5, 1, 4, 8, 12, 12, 1, 5, 13, 24, 32, 32, 1, 6, 18, 43, 73, 94, 94, 1, 7, 25, 69, 141, 227, 289, 289, 1, 8, 32, 104, 252, 480, 734, 910, 910, 1, 9, 41, 150, 414, 920, 1656, 2430, 2934, 2934, 1, 10, 50, 207, 649, 1636, 3370, 5744, 8150, 9686, 9686, 1, 11

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OFFSET

1,5

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..550

FORMULA

T(3,n) = A000982(n+1).

EXAMPLE

Table starts

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

....1....2.....3.....4......5......6......7.......8.......9......10......11

....2....5.....8....13.....18.....25.....32......41......50......61......72

....5...12....24....43.....69....104....150.....207.....277.....362.....462

...12...32....73...141....252....414....649.....967....1394....1944....2649

...32...94...227...480....920...1636...2739....4370....6698....9926...14293

...94..289...734..1656...3370...6375..11322...19138...30982...48417...73316

..289..910..2430..5744..12346..24591..46029...81805..139143..227930..361384

..910.2934..8150.20094..45207..94257.184717..343363..610358.1043534.1724882

.2934.9686.27718.70922.165821.360002.734517.1421530.2628824.4672836.8022362

Some solutions for n=7 and k=5:

.-7...-9...-8..-10...-6...-6...-9...-8...-8...-7...-9..-10...-9...-8...-9...-7

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

.-3...-1...-5...-4...-4...-3...-1...-4...-5...-2...-6...-3...-1...-3...-4...-3

.-1....0...-1....3...-3...-2....0...-1....0...-1....4....0....1....1...-1...-1

..3....3....2....5...-1....1....1....4....3....0....5....3....3....2....4....0

..4....4....8....6....9....7....4....5....7....4....6....5....4....5....6....7

..9...10...10....7...10....8....9...10...10....9....8...10....5...10....9....8

CROSSREFS

Column 1 is A076822.

Column 2 is A002838.

Cf. A000982.

Sequence in context: A257006 A363565 A139687 * A064581 A064580 A009766

Adjacent sequences: A188178 A188179 A188180 * A188182 A188183 A188184

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 23 2011

STATUS

approved