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%I #4 Feb 01 2015 10:49:36
%S 512,2384,2384,10240,10870,10240,37200,54212,54212,37200,116056,
%T 183210,312322,183210,116056,358324,536906,978154,978154,536906,
%U 358324,1029664,1612832,2647806,2148260,2647806,1612832,1029664,2800912,4205934,7796356
%N T(n,k)=Number of (n+2)X(k+2) 0..1 arrays with every 3X3 subblock sum of the four sums of the central row, central column, diagonal and antidiagonal nondecreasing horizontally and vertically
%C Table starts
%C ......512.....2384.....10240.....37200....116056.....358324....1029664
%C .....2384....10870.....54212....183210....536906....1612832....4205934
%C ....10240....54212....312322....978154...2647806....7796356...20277514
%C ....37200...183210....978154...2148260...4796417...12136355...25618602
%C ...116056...536906...2647806...4796417..10679860...25591173...45085796
%C ...358324..1612832...7796356..12136355..25591173...67038844..120967261
%C ..1029664..4205934..20277514..25618602..45085796..120967261..206491388
%C ..2800912.10525070..50757141..56219231.101378800..285405350..496247824
%C ..7536024.25843648.124775368.118029035.196258426..585731513..980309768
%C .19539824.60108505.293581128.245830679.401333712.1260737905.2140733638
%H R. H. Hardin, <a href="/A254568/b254568.txt">Table of n, a(n) for n = 1..1740</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 48] for n>50
%F k=2: [order 48] for n>56
%F k=3: [order 51] for n>61
%F k=4: [order 50] for n>62
%F k=5: [order 49] for n>63
%F k=6: [order 54] for n>70
%F k=7: [order 53] for n>71
%F Empirical quasipolynomials for column k:
%F k=2: polynomial of degree 20 plus a quasipolynomial of degree 12 with period 6 for n>8
%F k=3: polynomial of degree 21 plus a quasipolynomial of degree 13 with period 6 for n>10
%F k=4: polynomial of degree 22 plus a quasipolynomial of degree 12 with period 6 for n>12
%F k=5: polynomial of degree 23 plus a quasipolynomial of degree 11 with period 6 for n>14
%F k=6: polynomial of degree 24 plus a quasipolynomial of degree 13 with period 6 for n>16
%F k=7: polynomial of degree 25 plus a quasipolynomial of degree 12 with period 6 for n>18
%e Some solutions for n=2 k=4
%e ..0..0..0..1..0..0....0..0..0..0..0..1....0..0..0..1..0..1....0..0..0..0..0..0
%e ..0..0..0..0..1..0....1..0..0..0..1..0....0..0..0..1..1..1....0..0..0..1..1..0
%e ..0..0..0..0..1..0....0..1..1..1..1..1....1..1..1..1..1..0....1..0..1..1..1..1
%e ..0..1..1..1..1..1....0..1..1..0..0..1....0..1..0..1..1..1....1..1..0..0..0..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Feb 01 2015
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