%I #4 Dec 19 2014 11:34:12
%S 572,1013,687,1758,1684,1189,3162,4026,4226,2230,6598,8253,12840,
%T 10259,4382,13038,22701,29463,39492,28978,8697,24852,56953,110665,
%U 95904,145594,80304,17046,51396,121016,355574,448323,395940,527688,205127,34424
%N T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 3 4 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 3 4 6 or 7
%C Table starts
%C ....572....1013.....1758......3162.......6598........13038........24852
%C ....687....1684.....4026......8253......22701........56953.......121016
%C ...1189....4226....12840.....29463.....110665.......355574.......840655
%C ...2230...10259....39492.....95904.....448323......1848350......4416767
%C ...4382...28978...145594....395940....2641643.....14252070.....39238223
%C ...8697...80304...527688...1504636...13960830....101563107....285228944
%C ..17046..205127..1812508...5124134...62261756....625096361...1669555189
%C ..34424..598762..7013991..21431528..378997999...5008257261..14996577319
%C ..69196.1716412.27089549..82893234.2046478799..37697432955.109620130066
%C .136906.4519719.99843027.292817550.9628330801.249652077490.681798971770
%H R. H. Hardin, <a href="/A252640/b252640.txt">Table of n, a(n) for n = 1..648</a>
%F Empirical for column k:
%F k=1: [linear recurrence of order 18] for n>24
%F k=2: [order 27] for n>36
%F k=3: [order 33] for n>42
%F k=4: [order 27] for n>35
%F k=5: [order 36] for n>46
%F k=6: [order 51] for n>63
%F k=7: [order 39] for n>50
%F Empirical for row n:
%F n=1: [linear recurrence of order 67] for n>74
%F n=2: [order 60] for n>63
%F n=3: [order 60] for n>63
%F n=4: [order 60] for n>62
%F n=5: [order 90] for n>94
%e Some solutions for n=4 k=4
%e ..1..1..2..1..1..2....2..2..3..2..2..3....3..0..1..3..3..1....1..3..0..1..3..3
%e ..1..3..3..1..0..3....1..3..3..1..0..3....2..1..1..2..1..1....1..2..1..1..2..1
%e ..3..1..3..3..1..3....2..3..2..2..0..2....3..1..3..3..1..3....3..3..1..0..3..1
%e ..1..1..2..1..1..2....2..2..3..2..2..3....3..0..1..3..0..1....1..0..3..1..3..3
%e ..1..3..3..1..3..0....1..3..3..1..3..3....2..1..1..2..1..1....1..2..1..1..2..1
%e ..0..1..3..0..1..3....2..0..2..2..0..2....3..1..3..3..1..0....3..3..1..3..3..1
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Dec 19 2014