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

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A235310 T(n,k) is the number of (n+1) X (k+1) 0..5 arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 6 (constant-stress 1 X 1 tilings). 9
70, 210, 210, 518, 518, 518, 1554, 1106, 1106, 1554, 4006, 2918, 2118, 2918, 4006, 12018, 6786, 5042, 5042, 6786, 12018, 32006, 18662, 10790, 10790, 10790, 18662, 32006, 96018, 46226, 27602, 21090, 21090, 27602, 46226, 96018, 261670, 130598 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

      70    210     518    1554    4006   12018   32006   96018   261670

     210    518    1106    2918    6786   18662   46226  130598   338370

     518   1106    2118    5042   10790   27602   64326  172658   428198

    1554   2918    5042   10790   21090   49574  107186  269222   629154

    4006   6786   10790   21090   38182   83394  168998  400674   889126

   12018  18662   27602   49574   83394  168998  319826  711206  1486338

   32006  46226   64326  107186  168998  319826  568902 1192946  2360486

   96018 130598  172658  269222  400674  711206 1192946 2360486  4418658

  261670 338370  428198  629154  889126 1486338 2360486 4418658  7845670

  785010 973478 1187666 1656998 2238786 3544742 5359826 9528998 16106370

Empirical: T(n,k) is the number of (n+1) X (k+1) 0..4+i arrays with every 2 X 2 subblock having its diagonal sum differing from its antidiagonal sum by 4+2*i (constant-stress 1 X 1 tilings), for i=1..3(..?).

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..312

FORMULA

Empirical for column k (the k=2..7 recurrence also works for k=1; apparently all rows and columns satisfy the same order 14 recurrence):

k=1: a(n) = 3*a(n-1) +13*a(n-2) -39*a(n-3) -40*a(n-4) +120*a(n-5)

k=2..7: [same order 14 recurrence]

EXAMPLE

Some solutions for n=5, k=4:

  0 3 0 4 0     5 2 5 2 5     3 5 0 5 3     5 1 5 2 5

  5 2 5 3 5     2 5 2 5 2     4 0 1 0 4     0 2 0 3 0

  1 4 1 5 1     3 0 3 0 3     3 5 0 5 3     4 0 4 1 4

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

  0 3 0 4 0     3 0 3 0 3     3 5 0 5 3     4 0 4 1 4

  4 1 4 2 4     1 4 1 4 1     5 1 2 1 5     1 3 1 4 1

CROSSREFS

Sequence in context: A165762 A165764 A153669 * A235303 A234564 A234557

Adjacent sequences:  A235307 A235308 A235309 * A235311 A235312 A235313

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 05 2014

STATUS

approved

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified August 14 15:34 EDT 2022. Contains 356122 sequences. (Running on oeis4.)