A200990 - OEIS

A200990

T(n,k)=Number of nXk 0..4 arrays with every row and column nondecreasing rightwards and downwards, and the number of instances of each value within one of each other

5, 10, 10, 10, 10, 10, 5, 20, 20, 5, 1, 79, 92, 79, 1, 5, 21, 537, 537, 21, 5, 10, 226, 140, 1225, 140, 226, 10, 10, 157, 3157, 1095, 1095, 3157, 157, 10, 5, 227, 3604, 15023, 4919, 15023, 3604, 227, 5, 1, 678, 6692, 95845, 27000, 27000, 95845, 6692, 678, 1, 5, 120

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Table starts

..5..10....10......5.......1........5.........10..........10...........5

.10..10....20.....79......21......226........157.........227.........678

.10..20....92....537.....140.....3157.......3604........6692.......26168

..5..79...537...1225....1095....15023......95845......268375......325061

..1..21...140...1095....4919....27000......97341......383172.....1188521

..5.226..3157..15023...27000...752271....8434277....39361323....80878071

.10.157..3604..95845...97341..8434277...29555346...171588826..1801771085

.10.227..6692.268375..383172.39361323..171588826..1278883650.16557969007

..5.678.26168.325061.1188521.80878071.1801771085.16557969007.65182166083

..1.120..5408.168262.3704820.64001290..853004113..9528745293.89750034774

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

T(n,1) = binomial(5,n modulo 5). For a 0..z array, T(n,1) = binomial(z+1, n modulo (z+1)).

EXAMPLE

Some solutions for n=5 k=3

..0..1..2....0..0..2....0..1..2....0..0..1....0..0..0....0..1..1....0..0..0

..0..1..3....0..1..2....0..1..2....0..1..3....1..1..2....0..1..2....1..1..1

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

..2..2..4....1..3..4....3..3..4....2..2..3....2..3..3....2..3..4....2..3..4

..3..3..4....2..3..4....3..4..4....4..4..4....4..4..4....2..4..4....2..3..4

CROSSREFS

Column 1 for a 0..z array is binomial(z+1,n modulo (z+1))

Sequence in context: A065755 A346007 A135912 * A040020 A222181 A282172

Adjacent sequences: A200987 A200988 A200989 * A200991 A200992 A200993

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin Nov 25 2011

STATUS

approved