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%I #4 Feb 01 2015 19:24:52
%S 512,2868,2868,15051,17125,15051,72939,96756,110259,72939,332330,
%T 545360,774168,649029,332330,1451174,3083065,5909527,5852880,3699505,
%U 1451174,6117882,17163021,45867931,58920922,42278366,20636376,6117882,25078442
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the two medians of the central row and the central column and the two maximums of the diagonal and antidiagonal nondecreasing horizontally, vertically and ne-to-sw antidiagonally
%C Table starts
%C ......512......2868.......15051........72939.........332330.........1451174
%C .....2868.....17125.......96756.......545360........3083065........17163021
%C ....15051....110259......774168......5909527.......45867931.......350562134
%C ....72939....649029.....5852880.....58920922......613720640......6258245316
%C ...332330...3699505....42278366....548753241.....7610621332....103508337281
%C ..1451174..20636376...305579066...5184793937....96984109170...1782085332862
%C ..6117882.113625185..2204567802..49094787979..1242236438386..30739517451493
%C .25078442.620711336.15863354126.464109388554.15846867693636.527044893827218
%H R. H. Hardin, <a href="/A254586/b254586.txt">Table of n, a(n) for n = 1..311</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 26] for n>27
%F k=2: [order 25] for n>30
%F k=3: [order 18] for n>25
%F k=4: [order 25] for n>32
%F k=5: [order 38] for n>46
%F k=6: [order 63] for n>72
%F Empirical for row n:
%F n=1: [same linear recurrence of order 26] for n>27
%F n=2: [order 49] for n>55
%F n=3: [order 66] for n>81
%e Some solutions for n=2 k=4
%e ..1..1..0..1..0..1....1..0..1..0..1..0....0..0..0..1..0..1....0..0..1..0..0..1
%e ..0..0..1..1..1..1....0..0..0..0..0..1....0..1..0..0..0..1....0..0..0..0..1..1
%e ..0..1..0..1..1..1....0..1..0..1..1..1....1..0..0..1..1..0....0..0..0..1..1..1
%e ..1..1..1..1..1..0....0..1..0..1..1..0....0..1..1..1..1..0....0..0..1..1..0..0
%Y Column 1 and row 1 are A254354
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 01 2015