The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A186180 T(n,k)=Number of (n+2)X(k+2) 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order 10

%I #8 Dec 09 2018 12:09:00

%S 520017,10084236,10084236,143369699,311128593,143369699,1662436696,

%T 6520730198,6520730198,1662436696,16382439469,105970767207,

%U 188034884094,105970767207,16382439469,140871930232,1414199542732,4041778238254

%N T(n,k)=Number of (n+2)X(k+2) 0..5 arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order

%C Table starts

%C ..........520017..........10084236............143369699............1662436696

%C ........10084236.........311128593...........6520730198..........105970767207

%C .......143369699........6520730198.........188034884094.........4041778238254

%C ......1662436696......105970767207........4041778238254.......111203560772547

%C .....16382439469.....1414199542732.......69471558136868......2391923493659465

%C ....140871930232....16059530994398......995828085723859.....42174821764604242

%C ...1078197169699...159099595031390....12251749347425002....629512200937395977

%C ...7459396065112..1400823449171621...132151619698400257...8143852416376007571

%C ..47221234070168.11121210203531892..1270399513311212137..92981285763140685886

%C .276218909139304.80539662788823416.11027904404610778911.950506396177707075676

%H R. H. Hardin, <a href="/A186180/b186180.txt">Table of n, a(n) for n = 1..178</a>

%H R. H. Hardin, <a href="/A186180/a186180.txt">Polynomials for columns 1-5</a>

%F Empirical: T(n,k) is a polynomial of degree 5k+50 in n, for fixed k.

%F Let T(n,k,z) be the number of (n+2)X(k+2) 0..z arrays with each 3X3 subblock having rows and columns in lexicographically nondecreasing order.

%F Then empirically T(n,k,z) is a polynomial of degree z*k + z*(z+1)*(z+5)/6 in n, for fixed k.

%e Some solutions for 5X4

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

%e ..0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0....0..0..0..0

%e ..0..0..0..3....0..0..0..0....0..0..0..0....0..0..0..3....0..0..0..0

%e ..0..0..0..5....0..0..1..2....0..1..1..4....0..1..5..1....0..0..2..3

%e ..0..1..1..0....1..2..0..2....3..1..4..1....5..4..4..5....0..2..5..1

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, General degree formula intuited by _D. S. McNeil_ in the Sequence Fans Mailing List, Feb 13 2011

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 3 18:52 EST 2023. Contains 367540 sequences. (Running on oeis4.)