cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A184137 T(n,k)=Number of nXk 0..2 arrays with rows and columns in nondecreasing order.

Original entry on oeis.org

3, 6, 6, 10, 29, 10, 15, 112, 112, 15, 21, 356, 1169, 356, 21, 28, 972, 10020, 10020, 972, 28, 36, 2359, 70243, 250841, 70243, 2359, 36, 45, 5217, 414848, 5136783, 5136783, 414848, 5217, 45, 55, 10704, 2126064, 86649029, 318174607, 86649029, 2126064
Offset: 1

Views

Author

R. H. Hardin Jan 09 2011

Keywords

Comments

Empirical: T(n,k) for elements in 0..z is a polynomial in n of degree ((z+1)^k)-1 for fixed k
Table starts
..3.....6........10............15................21....................28
..6....29.......112...........356...............972..................2359
.10...112......1169.........10020.............70243................414848
.15...356.....10020........250841...........5136783..............86649029
.21...972.....70243.......5136783.........318174607...........16226388113
.28..2359....414848......86649029.......16226388113.........2533164987353
.36..5217...2126064....1235699769......692646032166.......330480778987068
.45.10704...9681099...15270848022....25325301730396.....36743249714104252
.55.20647..39886396..166834456961...809428667338479...3551368791876387512
.66.37818.150795172.1636866521557.22988798937359989.303434279544306336607

Examples

			Some solutions for 4X3
..0..1..2....0..0..0....0..1..2....0..1..2....0..0..2....0..0..0....1..1..2
..1..0..2....0..0..1....1..0..2....1..1..2....0..0..2....0..0..1....1..2..2
..2..0..0....0..0..2....2..1..2....1..2..1....0..2..2....0..1..2....2..1..0
..2..0..1....2..2..0....2..2..1....1..2..1....2..1..1....0..2..1....2..1..0

Links

Crossrefs

Column 1 is A000217(n+1)
Diagonal is A162085

A229794 T(n,k)=Number of n X n 0..k arrays with rows and columns in lexicographically nondecreasing order.

Original entry on oeis.org

2, 3, 7, 4, 29, 45, 5, 86, 1169, 650, 6, 205, 14178, 250841, 24520, 7, 421, 102251, 21907055, 318174607, 2625117, 8, 777, 520017, 733861607, 348053502590, 2533164987353, 836488618, 9, 1324, 2066505, 13111482259, 83399309397669
Offset: 1

Views

Author

R. H. Hardin, Sep 29 2013

Keywords

Comments

Table starts
.....2.........3............4..............5................6
.....7........29...........86............205..............421
....45......1169........14178.........102251...........520017
...650....250841.....21907055......733861607......13111482259
.24520.318174607.348053502590.83399309397669.7470491620551006

Examples

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

Links

Crossrefs

Column 1 is A089006
Column 2 is A162085
Column 3 is A162086
Column 4 is A162087
Column 5 is A162088
Column 6 is A162089
Column 7 is A162090

Formula

Empirical for row n:
n=1: a(n) = 1*n + 1
n=2: a(n) = (1/3)*n^4 + (7/6)*n^3 + (13/6)*n^2 + (7/3)*n + 1
n=3: [polynomial of degree 9]
n=4: [polynomial of degree 16]
Showing 1-2 of 2 results.

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