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A278727 T(n,k)=Number of nXk 0..3 arrays with rows in nondecreasing lexicographic order and columns in nonincreasing lexicographic order. 7
4, 10, 10, 20, 60, 20, 35, 275, 275, 35, 56, 1050, 3232, 1050, 56, 84, 3492, 33466, 33466, 3492, 84, 120, 10401, 306070, 1058494, 306070, 10401, 120, 165, 28288, 2487889, 30942600, 30942600, 2487889, 28288, 165, 220, 71266, 18151220, 815294800 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

...4.....10........20............35.................56.....................84

..10.....60.......275..........1050...............3492..................10401

..20....275......3232.........33466.............306070................2487889

..35...1050.....33466.......1058494...........30942600..............815294800

..56...3492....306070......30942600.........3062815568...........279368748599

..84..10401...2487889.....815294800.......279368748599.........90462380211862

.120..28288..18151220...19328645044.....23161560633508......26947618206791521

.165..71266.120104810..414671691083...1747727428639023....7361981179311574929

.220.168155.727684612.8109321869307.120668752462156921.1850980180963910285369

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..111

FORMULA

Empirical for column k:

k=1: a(n) = (1/6)*n^3 + 1*n^2 + (11/6)*n + 1

k=2: [polynomial of degree 12]

k=3: [polynomial of degree 45]

EXAMPLE

Some solutions for n=3 k=4

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

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

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

CROSSREFS

Column 1 is A000292(n+1).

Diagonal is A229771.

Sequence in context: A310335 A310336 A227060 * A184129 A202581 A201729

Adjacent sequences:  A278724 A278725 A278726 * A278728 A278729 A278730

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 27 2016

STATUS

approved

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Last modified October 24 19:46 EDT 2020. Contains 338009 sequences. (Running on oeis4.)