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A252532 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 3 6 or 7.

%I A252532 #6 Jun 02 2025 11:20:06
%S A252532 750,730,595,621,337,460,719,341,334,535,778,462,466,426,546,932,706,
%T A252532 626,610,676,649,1200,1000,1120,790,1114,964,823,1498,1468,1760,1592,
%U A252532 1676,1748,1344,1036,1968,2420,2404,2440,4420,2504,2332,2312,1328,2708,3480
%N A252532 T(n,k)=Number of (n+2)X(k+2) 0..3 arrays with every 3X3 subblock row and diagonal sum equal to 0 2 3 6 or 7 and every 3X3 column and antidiagonal sum not equal to 0 2 3 6 or 7.
%C A252532 Table starts
%C A252532 ..750..730..621...719...778....932...1200....1498....1968....2708.....3473
%C A252532 ..595..337..341...462...706...1000...1468....2420....3480....5240.....8872
%C A252532 ..460..334..466...626..1120...1760...2404....4304....6832....9416....16864
%C A252532 ..535..426..610...790..1592...2440...3160....6368....9760...12640....25472
%C A252532 ..546..676.1114..1676..4420...7184..11456...31136...50560...83840...232192
%C A252532 ..649..964.1748..2504..7136..13184..19232...54656..102272..150656...427520
%C A252532 ..823.1344.2332..3160.10720..18656..25280...85760..149248..202240...686080
%C A252532 .1036.2312.4244..6704.30752..54464..91648..433664..763904.1341440..6471680
%C A252532 .1328.3336.6760.10016.49792.101888.153856..760832.1580032.2410496.11886592
%C A252532 .1756.4800.9112.12640.77696.145792.202240.1243136.2332672.3235840.19890176
%H A252532 R. H. Hardin, <a href="/A252532/b252532.txt">Table of n, a(n) for n = 1..612</a>
%F A252532 Empirical for column k:
%F A252532 k=1: a(n) = 4*a(n-3) -3*a(n-6) -4*a(n-9) +4*a(n-12) for n>23
%F A252532 k=2: a(n) = 6*a(n-3) -8*a(n-6) for n>10
%F A252532 k=3: a(n) = 6*a(n-3) -8*a(n-6) for n>8
%F A252532 k=4: a(n) = 4*a(n-3) for n>5
%F A252532 k=5: a(n) = 12*a(n-3) -32*a(n-6) for n>8
%F A252532 k=6: a(n) = 12*a(n-3) -32*a(n-6) for n>8
%F A252532 k=7: a(n) = 8*a(n-3) for n>5
%F A252532 Empirical for row n:
%F A252532 n=1: a(n) = 4*a(n-3) -3*a(n-6) -4*a(n-9) +4*a(n-12) for n>39
%F A252532 n=2: a(n) = 6*a(n-3) -8*a(n-6) for n>10
%F A252532 n=3: a(n) = 6*a(n-3) -8*a(n-6) for n>8
%F A252532 n=4: a(n) = 4*a(n-3) for n>5
%F A252532 n=5: a(n) = 12*a(n-3) -32*a(n-6) for n>8
%F A252532 n=6: a(n) = 12*a(n-3) -32*a(n-6) for n>8
%F A252532 n=7: a(n) = 8*a(n-3) for n>5
%e A252532 Some solutions for n=4 k=4
%e A252532 ..2..2..3..2..2..3....1..1..0..1..1..0....3..2..2..3..2..2....0..2..1..0..1..1
%e A252532 ..3..2..2..3..2..2....2..0..0..3..0..0....3..0..3..3..0..3....0..2..0..0..3..3
%e A252532 ..3..0..3..3..0..3....1..0..1..1..0..1....2..2..3..2..2..3....1..1..0..1..1..0
%e A252532 ..2..2..3..2..2..3....1..1..0..1..1..0....3..2..2..3..2..2....0..1..1..0..1..1
%e A252532 ..3..2..2..3..2..2....3..0..0..2..0..0....3..1..3..3..0..3....0..3..0..0..3..0
%e A252532 ..0..0..3..3..1..3....1..0..1..1..0..1....2..2..3..2..2..3....1..1..0..1..1..0
%K A252532 nonn,tabl
%O A252532 1,1
%A A252532 _R. H. Hardin_, Dec 18 2014