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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 8
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

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Last modified September 18 15:44 EDT 2021. Contains 347527 sequences. (Running on oeis4.)