A235565 - OEIS

%I #6 Apr 17 2022 21:56:13

%S 81,537,537,3199,8345,3199,17837,113391,113391,17837,95679,1383617,

%T 3793647,1383617,95679,498597,15633605,114840543,114840543,15633605,

%U 498597,2546207,165947729,3160338477,9226436673,3160338477,165947729

%N T(n,k) = Number of (n+1) X (k+1) 0..2 arrays with the difference of the upper and lower median value of each 2 X 2 subblock in lexicographically nondecreasing order rowwise and columnwise.

%C Table starts

%C ........81..........537...........3199............17837.............95679

%C .......537.........8345.........113391..........1383617..........15633605

%C ......3199.......113391........3793647........114840543........3160338477

%C .....17837......1383617......114840543.......9226436673......682927935295

%C .....95679.....15633605.....3160338477.....682927935295...142306326935545

%C ....498597....165947729....79254774059...45560931506381.27003055042316513

%C ...2546207...1680360507..1838291205271.2748535870959415

%C ..12796069..16368643767.39837425003517

%C ..63520287.154629524369

%C .312150917

%H R. H. Hardin, <a href="/A235565/b235565.txt">Table of n, a(n) for n = 1..60</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 10],

%F k=2: [order 67].

%e Some solutions for n=2, k=4

%e ..0..0..1..0..0....0..0..0..0..1....0..0..1..0..2....0..0..0..2..2

%e ..0..1..2..1..2....1..0..0..0..2....2..0..0..1..2....0..0..0..0..1

%e ..1..1..1..0..2....1..2..2..2..2....0..0..0..2..1....2..1..1..1..0

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 12 2014