%I #6 Apr 17 2022 23:03:14

%S 512,2812,2812,12616,14681,12616,54236,72644,59531,54236,236024,

%T 382316,268900,223357,236024,1021428,1989857,1420232,718226,888391,

%U 1021428,4351908,10193041,7815717,2983064,2192422,3647288,4351908,18369164

%N T(n,k) = Number of (n+2) X (k+2) 0..1 arrays with every 3 X 3 subblock sum of the two maximums of the diagonal and antidiagonal minus the sum of the minimums of the central row and column nondecreasing horizontally, vertically and ne-to-sw antidiagonally.

%C Table starts

%C .......512.......2812.....12616......54236.....236024.....1021428......4351908

%C ......2812......14681.....72644.....382316....1989857....10193041.....52034327

%C .....12616......59531....268900....1420232....7815717....43088793....240716320

%C .....54236.....223357....718226....2983064...12249828....49369118....197326142

%C ....236024.....888391...2192422....9308828...35691048...159041102....742483152

%C ...1021428....3647288...6729896...29231312...87535036...325742026...1249946456

%C ...4351908...15380009..21120938...98883824..214982444...933774220...3756830312

%C ..18369164...65954108..68298122..378114160..718305580..3391678348..14833693096

%C ..77344420..284203166.216717474.1430424048.1845854060..9927463676..43837197480

%C .325241108.1230877185.690324184.5564609520.5194299052.34363573228.151675299240

%H R. H. Hardin, <a href="/A254260/b254260.txt">Table of n, a(n) for n = 1..638</a>

%F Empirical for column k:

%F k=1: [linear recurrence of order 17],

%F k=2: [order 21] for n>25,

%F k=3: [order 13] for n>19,

%F k=4: [order 12] for n>18,

%F k=5: [order 14] for n>21,

%F k=6: [order 12] for n>20,

%F k=7: [order 17] for n>25.

%F Empirical for row n:

%F n=1: [same linear recurrence of order 17],

%F n=2: [order 32] for n>37,

%F n=3: [order 41] for n>47,

%F n=4: [order 41] for n>50,

%F n=5: [order 47] for n>58,

%F n=6: [order 53] for n>67,

%F n=7: [order 65] for n>82.

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

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

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

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

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

%K nonn,tabl

%O 1,1

%A _R. H. Hardin_, Jan 27 2015