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%I #22 Jan 01 2023 09:47:00
%S 5,11,11,21,35,21,43,93,93,43,85,269,314,269,85,171,747,1213,1213,747,
%T 171,341,2115,4375,6427,4375,2115,341,683,5933,16334,31387,31387,
%U 16334,5933,683,1365,16717,59925,159651,202841,159651,59925,16717,1365,2731
%N T(n,k) = Half the number of (n+1) X (k+1) 0..2 arrays with every 2 X 2 subblock diagonal sum differing from its antidiagonal sum by more than 2.
%C T(n,k) apparently is also the number of ways to tile an (n+2) X (k+2) rectangle with 1 X 1 and 2 X 2 tiles.
%H R. H. Hardin, <a href="/A179618/b179618.txt">Table of n, a(n) for n = 1..839</a>
%e Table starts
%e 5 11 21 43 85 171 341
%e 11 35 93 269 747 2115 5933
%e 21 93 314 1213 4375 16334 59925
%e 43 269 1213 6427 31387 159651 795611
%e 85 747 4375 31387 202841 1382259 9167119
%e 171 2115 16334 159651 1382259 12727570 113555791
%e 341 5933 59925 795611 9167119 113555791 1355115601
%e 683 16717 221799 4005785 61643709 1029574631 16484061769
%e 1365 47003 817280 20064827 411595537 9258357134 198549329897
%e 2731 132291 3018301 100764343 2758179839 83605623809 2403674442213
%e Some solutions for 6 X 6:
%e 0 2 0 2 0 2 0 1 0 2 1 2 0 2 0 2 0 2 0 1 0 2 0 1
%e 2 0 2 0 2 1 2 0 2 0 2 0 2 0 1 0 1 0 2 0 2 0 2 0
%e 0 2 0 2 0 2 1 2 1 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2
%e 2 0 2 0 2 1 2 0 2 0 1 0 1 0 2 0 2 0 1 0 2 0 2 0
%e 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 1 2 1 2
%e 1 0 1 0 1 0 2 1 2 1 2 0 2 1 2 1 2 1 2 0 2 0 2 0
%Y Diagonal is A063443(n+2).
%Y Column 1 is A001045(n+3).
%Y Column 2 is A054854(n+2).
%Y Column 3 is A054855(n+2).
%Y Column 4 is A063650(n+2).
%Y Column 5 is A063651(n+2).
%Y Column 6 is A063652(n+2).
%Y Column 7 is A063653(n+2).
%Y Column 8 is A063654(n+2).
%K nonn,tabl
%O 1,1
%A _R. H. Hardin_, Jan 10 2011
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